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+Internet Research Task Force (IRTF)                         W. Kozlowski
+Request for Comments: 9340                                     S. Wehner
+Category: Informational                                           QuTech
+ISSN: 2070-1721                                             R. Van Meter
+                                                         Keio University
+                                                              B. Rijsman
+                                                              Individual
+                                                       A. S. Cacciapuoti
+                                                              M. Caleffi
+                                        University of Naples Federico II
+                                                             S. Nagayama
+                                                           Mercari, Inc.
+                                                              March 2023
+
+
+            Architectural Principles for a Quantum Internet
+
+Abstract
+
+   The vision of a quantum internet is to enhance existing Internet
+   technology by enabling quantum communication between any two points
+   on Earth.  To achieve this goal, a quantum network stack should be
+   built from the ground up to account for the fundamentally new
+   properties of quantum entanglement.  The first quantum entanglement
+   networks have been realised, but there is no practical proposal for
+   how to organise, utilise, and manage such networks.  In this
+   document, we attempt to lay down the framework and introduce some
+   basic architectural principles for a quantum internet.  This is
+   intended for general guidance and general interest.  It is also
+   intended to provide a foundation for discussion between physicists
+   and network specialists.  This document is a product of the Quantum
+   Internet Research Group (QIRG).
+
+Status of This Memo
+
+   This document is not an Internet Standards Track specification; it is
+   published for informational purposes.
+
+   This document is a product of the Internet Research Task Force
+   (IRTF).  The IRTF publishes the results of Internet-related research
+   and development activities.  These results might not be suitable for
+   deployment.  This RFC represents the consensus of the Quantum
+   Internet Research Group of the Internet Research Task Force (IRTF).
+   Documents approved for publication by the IRSG are not candidates for
+   any level of Internet Standard; see Section 2 of RFC 7841.
+
+   Information about the current status of this document, any errata,
+   and how to provide feedback on it may be obtained at
+   https://www.rfc-editor.org/info/rfc9340.
+
+Copyright Notice
+
+   Copyright (c) 2023 IETF Trust and the persons identified as the
+   document authors.  All rights reserved.
+
+   This document is subject to BCP 78 and the IETF Trust's Legal
+   Provisions Relating to IETF Documents
+   (https://trustee.ietf.org/license-info) in effect on the date of
+   publication of this document.  Please review these documents
+   carefully, as they describe your rights and restrictions with respect
+   to this document.
+
+Table of Contents
+
+   1.  Introduction
+   2.  Quantum Information
+     2.1.  Quantum State
+     2.2.  Qubit
+     2.3.  Multiple Qubits
+   3.  Entanglement as the Fundamental Resource
+   4.  Achieving Quantum Connectivity
+     4.1.  Challenges
+       4.1.1.  The Measurement Problem
+       4.1.2.  No-Cloning Theorem
+       4.1.3.  Fidelity
+       4.1.4.  Inadequacy of Direct Transmission
+     4.2.  Bell Pairs
+     4.3.  Teleportation
+     4.4.  The Life Cycle of Entanglement
+       4.4.1.  Elementary Link Generation
+       4.4.2.  Entanglement Swapping
+       4.4.3.  Error Management
+       4.4.4.  Delivery
+   5.  Architecture of a Quantum Internet
+     5.1.  Challenges
+     5.2.  Classical Communication
+     5.3.  Abstract Model of the Network
+       5.3.1.  The Control Plane and the Data Plane
+       5.3.2.  Elements of a Quantum Network
+       5.3.3.  Putting It All Together
+     5.4.  Physical Constraints
+       5.4.1.  Memory Lifetimes
+       5.4.2.  Rates
+       5.4.3.  Communication Qubits
+       5.4.4.  Homogeneity
+   6.  Architectural Principles
+     6.1.  Goals of a Quantum Internet
+     6.2.  The Principles of a Quantum Internet
+   7.  A Thought Experiment Inspired by Classical Networks
+   8.  Security Considerations
+   9.  IANA Considerations
+   10. Informative References
+   Acknowledgements
+   Authors' Addresses
+
+1.  Introduction
+
+   Quantum networks are distributed systems of quantum devices that
+   utilise fundamental quantum mechanical phenomena such as
+   superposition, entanglement, and quantum measurement to achieve
+   capabilities beyond what is possible with non-quantum (classical)
+   networks [Kimble08].  Depending on the stage of a quantum network
+   [Wehner18], such devices may range from simple photonic devices
+   capable of preparing and measuring only one quantum bit (qubit) at a
+   time all the way to large-scale quantum computers of the future.  A
+   quantum network is not meant to replace classical networks but rather
+   to form an overall hybrid classical-quantum network supporting new
+   capabilities that are otherwise impossible to realise [VanMeterBook].
+   For example, the most well-known application of quantum
+   communication, Quantum Key Distribution (QKD) [QKD], can create and
+   distribute a pair of symmetric encryption keys in such a way that the
+   security of the entire process relies on the laws of physics (and
+   thus can be mathematically proven to be unbreakable) rather than the
+   intractability of certain mathematical problems [Bennett14]
+   [Ekert91].  Small networks capable of QKD have even already been
+   deployed at short (roughly 100-kilometre) distances [Elliott03]
+   [Peev09] [Aguado19] [Joshi20].
+
+   The quantum networking paradigm also offers promise for a range of
+   new applications beyond quantum cryptography, such as distributed
+   quantum computation [Cirac99] [Crepeau02]; secure quantum computing
+   in the cloud [Fitzsimons17]; quantum-enhanced measurement networks
+   [Giovannetti04]; or higher-precision, long-baseline telescopes
+   [Gottesman12].  These applications are much more demanding than QKD,
+   and networks capable of executing them are in their infancy.  The
+   first fully quantum, multinode network capable of sending, receiving,
+   and manipulating distributed quantum information has only recently
+   been realised [Pompili21.1].
+
+   Whilst a lot of effort has gone into physically realising and
+   connecting such devices, and making improvements to their speed and
+   error tolerance, no proposals for how to run these networks have been
+   worked out at the time of this writing.  To draw an analogy with a
+   classical network, we are at a stage where we can start to physically
+   connect our devices and send data, but all sending, receiving, buffer
+   management, connection synchronisation, and so on must be managed by
+   the application directly by using low-level, custom-built, and
+   hardware-specific interfaces, rather than being managed by a network
+   stack that exposes a convenient high-level interface, such as
+   sockets.  Only recently was the first-ever attempt at such a network
+   stack experimentally demonstrated in a laboratory setting
+   [Pompili21.2].  Furthermore, whilst physical mechanisms for
+   transmitting quantum information exist, there are no robust protocols
+   for managing such transmissions.
+
+   This document, produced by the Quantum Internet Research Group
+   (QIRG), introduces quantum networks and presents general guidelines
+   for the design and construction of such networks.  Overall, it is
+   intended as an introduction to the subject for network engineers and
+   researchers.  It should not be considered as a conclusive statement
+   on how quantum networks should or will be implemented.  This document
+   was discussed on the QIRG mailing list and several IETF meetings.  It
+   represents the consensus of the QIRG members, of both experts in the
+   subject matter (from the quantum and networking domains) and
+   newcomers who are the target audience.
+
+2.  Quantum Information
+
+   In order to understand the framework for quantum networking, a basic
+   understanding of quantum information theory is necessary.  The
+   following sections aim to introduce the minimum amount of knowledge
+   necessary to understand the principles of operation of a quantum
+   network.  This exposition was written with a classical networking
+   audience in mind.  It is assumed that the reader has never before
+   been exposed to any quantum physics.  We refer the reader to
+   [SutorBook] and [NielsenChuang] for an in-depth introduction to
+   quantum information systems.
+
+2.1.  Quantum State
+
+   A quantum mechanical system is described by its quantum state.  A
+   quantum state is an abstract object that provides a complete
+   description of the system at that particular moment.  When combined
+   with the rules of the system's evolution in time, such as a quantum
+   circuit, it also then provides a complete description of the system
+   at all times.  For the purposes of computing and networking, the
+   classical equivalent of a quantum state would be a string or stream
+   of logical bit values.  These bits provide a complete description of
+   what values we can read out from that string at that particular
+   moment, and when combined with its rules for evolution in time, such
+   as a logical circuit, we will also know its value at any other time.
+
+   Just like a single classical bit, a quantum mechanical system can be
+   simple and consist of a single particle, e.g., an atom or a photon of
+   light.  In this case, the quantum state provides the complete
+   description of that one particle.  Similarly, just like a string of
+   bits consists of multiple bits, a single quantum state can be used to
+   also describe an ensemble of many particles.  However, because
+   quantum states are governed by the laws of quantum mechanics, their
+   behaviour is significantly different to that of a string of bits.  In
+   this section, we will summarise the key concepts to understand these
+   differences.  We will then explain their consequences for networking
+   in the rest of this document.
+
+2.2.  Qubit
+
+   The differences between quantum computation and classical computation
+   begin at the bit level.  A classical computer operates on the binary
+   alphabet { 0, 1 }.  A quantum bit, called a qubit, exists over the
+   same binary space, but unlike the classical bit, its state can exist
+   in a superposition of the two possibilities:
+
+   |qubit⟩ = a |0⟩ + b |1⟩,
+
+   where |X⟩ is Dirac's ket notation for a quantum state (the value that
+   a qubit holds) -- here, the binary 0 and 1 -- and the coefficients a
+   and b are complex numbers called probability amplitudes.  Physically,
+   such a state can be realised using a variety of different
+   technologies such as electron spin, photon polarisation, atomic
+   energy levels, and so on.
+
+   Upon measurement, the qubit loses its superposition and irreversibly
+   collapses into one of the two basis states, either |0⟩ or |1⟩. Which
+   of the two states it ends up in may not be deterministic but can be
+   determined from the readout of the measurement.  The measurement
+   result is a classical bit, 0 or 1, corresponding to |0⟩ and |1⟩,
+   respectively.  The probability of measuring the state in the |0⟩
+   state is |a|^2; similarly, the probability of measuring the state in
+   the |1⟩ state is |b|^2, where |a|^2 + |b|^2 = 1.  This randomness is
+   not due to our ignorance of the underlying mechanisms but rather is a
+   fundamental feature of a quantum mechanical system [Aspect81].
+
+   The superposition property plays an important role in fundamental
+   gate operations on qubits.  Since a qubit can exist in a
+   superposition of its basis states, the elementary quantum gates are
+   able to act on all states of the superposition at the same time.  For
+   example, consider the NOT gate:
+
+   NOT (a |0⟩ + b |1⟩) → a |1⟩ + b |0⟩.
+
+   It is important to note that "qubit" can have two meanings.  In the
+   first meaning, "qubit" refers to a physical quantum *system* whose
+   quantum state can be expressed as a superposition of two basis
+   states, which we often label |0⟩ and |1⟩. Here, "qubit" refers to a
+   physical implementation akin to what a flip-flop, switch, voltage, or
+   current would be for a classical bit.  In the second meaning, "qubit"
+   refers to the abstract quantum *state* of a quantum system with such
+   two basis states.  In this case, the meaning of "qubit" is akin to
+   the logical value of a bit, from classical computing, i.e., "logical
+   0" or "logical 1".  The two concepts are related, because a physical
+   "qubit" (first meaning) can be used to store the abstract "qubit"
+   (second meaning).  Both meanings are used interchangeably in
+   literature, and the meaning is generally clear from the context.
+
+2.3.  Multiple Qubits
+
+   When multiple qubits are combined in a single quantum state, the
+   space of possible states grows exponentially and all these states can
+   coexist in a superposition.  For example, the general form of a two-
+   qubit register is
+
+   a |00⟩ + b |01⟩ + c |10⟩ + d |11⟩,
+
+   where the coefficients have the same probability amplitude
+   interpretation as for the single-qubit state.  Each state represents
+   a possible outcome of a measurement of the two-qubit register.  For
+   example, |01⟩ denotes a state in which the first qubit is in the
+   state |0⟩ and the second is in the state |1⟩.
+
+   Performing single-qubit gates affects the relevant qubit in each of
+   the superposition states.  Similarly, two-qubit gates also act on all
+   the relevant superposition states, but their outcome is far more
+   interesting.
+
+   Consider a two-qubit register where the first qubit is in the
+   superposed state (|0⟩ + |1⟩)/sqrt(2) and the other is in the
+   state |0⟩.  This combined state can be written as
+
+   (|0⟩ + |1⟩)/sqrt(2) x |0⟩ = (|00⟩ + |10⟩)/sqrt(2),
+
+   where x denotes a tensor product (the mathematical mechanism for
+   combining quantum states together).
+
+   The constant 1/sqrt(2) is called the normalisation factor and
+   reflects the fact that the probabilities of measuring either a |0⟩ or
+   a |1⟩ for the first qubit add up to one.
+
+   Let us now consider the two-qubit Controlled NOT, or CNOT, gate.  The
+   CNOT gate takes as input two qubits -- a control and a target -- and
+   applies the NOT gate to the target if the control qubit is set.  The
+   truth table looks like
+
+                               +====+=====+
+                               | IN | OUT |
+                               +====+=====+
+                               | 00 |  00 |
+                               +----+-----+
+                               | 01 |  01 |
+                               +----+-----+
+                               | 10 |  11 |
+                               +----+-----+
+                               | 11 |  10 |
+                               +----+-----+
+
+                         Table 1: CNOT Truth Table
+
+   Now, consider performing a CNOT gate on the state with the first
+   qubit being the control.  We apply a two-qubit gate on all the
+   superposition states:
+
+   CNOT (|00⟩ + |10⟩)/sqrt(2) → (|00⟩ + |11⟩)/sqrt(2).
+
+   What is so interesting about this two-qubit gate operation?  The
+   final state is *entangled*.  There is no possible way of representing
+   that quantum state as a product of two individual qubits; they are no
+   longer independent.  That is, it is not possible to describe the
+   quantum state of either of the individual qubits in a way that is
+   independent of the other qubit.  Only the quantum state of the system
+   that consists of both qubits provides a physically complete
+   description of the two-qubit system.  The states of the two
+   individual qubits are now correlated beyond what is possible to
+   achieve classically.  Neither qubit is in a definite |0⟩ or |1⟩
+   state, but if we perform a measurement on either one, the outcome of
+   the partner qubit will *always* yield the exact same outcome.  The
+   final state, whether it's |00⟩ or |11⟩, is fundamentally random as
+   before, but the states of the two qubits following a measurement will
+   always be identical.  One can think of this as flipping two coins,
+   but both coins always land on "heads" or both land on "tails"
+   together -- something that we know is impossible classically.
+
+   Once a measurement is performed, the two qubits are once again
+   independent.  The final state is either |00⟩ or |11⟩, and both of
+   these states can be trivially decomposed into a product of two
+   individual qubits.  The entanglement has been consumed, and the
+   entangled state must be prepared again.
+
+3.  Entanglement as the Fundamental Resource
+
+   Entanglement is the fundamental building block of quantum networks.
+   Consider the state from the previous section:
+
+   (|00⟩ + |11⟩)/sqrt(2).
+
+   Neither of the two qubits is in a definite |0⟩ or |1⟩ state, and we
+   need to know the state of the entire register to be able to fully
+   describe the behaviour of the two qubits.
+
+   Entangled qubits have interesting non-local properties.  Consider
+   sending one of the qubits to another device.  This device could in
+   principle be anywhere: on the other side of the room, in a different
+   country, or even on a different planet.  Provided negligible noise
+   has been introduced, the two qubits will forever remain in the
+   entangled state until a measurement is performed.  The physical
+   distance does not matter at all for entanglement.
+
+   This lies at the heart of quantum networking, because it is possible
+   to leverage the non-classical correlations provided by entanglement
+   in order to design completely new types of application protocols that
+   are not possible to achieve with just classical communication.
+   Examples of such applications are quantum cryptography [Bennett14]
+   [Ekert91], blind quantum computation [Fitzsimons17], or distributed
+   quantum computation [Crepeau02].
+
+   Entanglement has two very special features from which one can derive
+   some intuition about the types of applications enabled by a quantum
+   network.
+
+   The first stems from the fact that entanglement enables stronger-
+   than-classical correlations, leading to opportunities for tasks that
+   require coordination.  As a trivial example, consider the problem of
+   consensus between two nodes who want to agree on the value of a
+   single bit.  They can use the quantum network to prepare the state
+   (|00⟩ + |11⟩)/sqrt(2) with each node holding one of the two qubits.
+   Once either of the two nodes performs a measurement, the state of the
+   two qubits collapses to either |00⟩ or |11⟩, so whilst the outcome is
+   random and does not exist before measurement, the two nodes will
+   always measure the same value.  We can also build the more general
+   multi-qubit state (|00...⟩ + |11...⟩)/sqrt(2) and perform the same
+   algorithm between an arbitrary number of nodes.  These stronger-than-
+   classical correlations generalise to measurement schemes that are
+   more complicated as well.
+
+   The second feature of entanglement is that it cannot be shared, in
+   the sense that if two qubits are maximally entangled with each other,
+   then it is physically impossible for these two qubits to also be
+   entangled with a third qubit [Terhal04].  Hence, entanglement forms a
+   sort of private and inherently untappable connection between two
+   nodes once established.
+
+   Entanglement is created through local interactions between two qubits
+   or as a product of the way the qubits were created (e.g., entangled
+   photon pairs).  To create a distributed entangled state, one can then
+   physically send one of the qubits to a remote node.  It is also
+   possible to directly entangle qubits that are physically separated,
+   but this still requires local interactions between some other qubits
+   that the separated qubits are initially entangled with.  Therefore,
+   it is the transmission of qubits that draws the line between a
+   genuine quantum network and a collection of quantum computers
+   connected over a classical network.
+
+   A quantum network is defined as a collection of nodes that is able to
+   exchange qubits and distribute entangled states amongst themselves.
+   A quantum node that is able only to communicate classically with
+   another quantum node is not a member of a quantum network.
+
+   Services and applications that are more complex can be built on top
+   of entangled states distributed by the network; for example, see
+   [ZOO].
+
+4.  Achieving Quantum Connectivity
+
+   This section explains the meaning of quantum connectivity and the
+   necessary physical processes at an abstract level.
+
+4.1.  Challenges
+
+   A quantum network cannot be built by simply extrapolating all the
+   classical models to their quantum analogues.  Sending qubits over a
+   wire like we send classical bits is simply not as easy to do.  There
+   are several technological as well as fundamental challenges that make
+   classical approaches unsuitable in a quantum context.
+
+4.1.1.  The Measurement Problem
+
+   In classical computers and networks, we can read out the bits stored
+   in memory at any time.  This is helpful for a variety of purposes
+   such as copying, error detection and correction, and so on.  This is
+   not possible with qubits.
+
+   A measurement of a qubit's state will destroy its superposition and
+   with it any entanglement it may have been part of.  Once a qubit is
+   being processed, it cannot be read out until a suitable point in the
+   computation, determined by the protocol handling the qubit, has been
+   reached.  Therefore, we cannot use the same methods known from
+   classical computing for the purposes of error detection and
+   correction.  Nevertheless, quantum error detection and correction
+   schemes exist that take this problem into account, and how a network
+   chooses to manage errors will have an impact on its architecture.
+
+4.1.2.  No-Cloning Theorem
+
+   Since directly reading the state of a qubit is not possible, one
+   could ask if we can simply copy a qubit without looking at it.
+   Unfortunately, this is fundamentally not possible in quantum
+   mechanics [Park70] [Wootters82].
+
+   The no-cloning theorem states that it is impossible to create an
+   identical copy of an arbitrary, unknown quantum state.  Therefore, it
+   is also impossible to use the same mechanisms that worked for
+   classical networks for signal amplification, retransmission, and so
+   on, as they all rely on the ability to copy the underlying data.
+   Since any physical channel will always be lossy, connecting nodes
+   within a quantum network is a challenging endeavour, and its
+   architecture must at its core address this very issue.
+
+4.1.3.  Fidelity
+
+   In general, it is expected that a classical packet arrives at its
+   destination without any errors introduced by hardware noise along the
+   way.  This is verified at various levels through a variety of error
+   detection and correction mechanisms.  Since we cannot read or copy a
+   quantum state, error detection and correction are more involved.
+
+   To describe the quality of a quantum state, a physical quantity
+   called fidelity is used [NielsenChuang].  Fidelity takes a value
+   between 0 and 1 -- higher is better, and less than 0.5 means the
+   state is unusable.  It measures how close a quantum state is to the
+   state we have tried to create.  It expresses the probability that the
+   state will behave exactly the same as our desired state.  Fidelity is
+   an important property of a quantum system that allows us to quantify
+   how much a particular state has been affected by noise from various
+   sources (gate errors, channel losses, environment noise).
+
+   Interestingly, quantum applications do not need perfect fidelity to
+   be able to execute -- as long as the fidelity is above some
+   application-specific threshold, they will simply operate at lower
+   rates.  Therefore, rather than trying to ensure that we always
+   deliver perfect states (a technologically challenging task),
+   applications will specify a minimum threshold for the fidelity, and
+   the network will try its best to deliver it.  A higher fidelity can
+   be achieved by either having hardware produce states of better
+   fidelity (sometimes one can sacrifice rate for higher fidelity) or
+   employing quantum error detection and correction mechanisms (see
+   [Mural16] and Chapter 11 of [VanMeterBook]).
+
+4.1.4.  Inadequacy of Direct Transmission
+
+   Conceptually, the most straightforward way to distribute an entangled
+   state is to simply transmit one of the qubits directly to the other
+   end across a series of nodes while performing sufficient forward
+   Quantum Error Correction (QEC) (Section 4.4.3.2) to bring losses down
+   to an acceptable level.  Despite the no-cloning theorem and the
+   inability to directly measure a quantum state, error-correcting
+   mechanisms for quantum communication exist [Jiang09] [Fowler10]
+   [Devitt13] [Mural16].  However, QEC makes very high demands on both
+   resources (physical qubits needed) and their initial fidelity.
+   Implementation is very challenging, and QEC is not expected to be
+   used until later generations of quantum networks are possible (see
+   Figure 2 of [Mural16] and Section 4.4.3.3 of this document).  Until
+   then, quantum networks rely on entanglement swapping (Section 4.4.2)
+   and teleportation (Section 4.3).  This alternative relies on the
+   observation that we do not need to be able to distribute any
+   arbitrary entangled quantum state.  We only need to be able to
+   distribute any one of what are known as the Bell pair states
+   [Briegel98].
+
+4.2.  Bell Pairs
+
+   Bell pair states are the entangled two-qubit states:
+
+            |00⟩ + |11⟩,
+            |00⟩ - |11⟩,
+            |01⟩ + |10⟩,
+            |01⟩ - |10⟩,
+
+   where the constant 1/sqrt(2) normalisation factor has been ignored
+   for clarity.  Any of the four Bell pair states above will do, as it
+   is possible to transform any Bell pair into another Bell pair with
+   local operations performed on only one of the qubits.  When each
+   qubit in a Bell pair is held by a separate node, either node can
+   apply a series of single-qubit gates to their qubit alone in order to
+   transform the state between the different variants.
+
+   Distributing a Bell pair between two nodes is much easier than
+   transmitting an arbitrary quantum state over a network.  Since the
+   state is known, handling errors becomes easier, and small-scale error
+   correction (such as entanglement distillation, as discussed in
+   Section 4.4.3.1), combined with reattempts, becomes a valid strategy.
+
+   The reason for using Bell pairs specifically as opposed to any other
+   two-qubit state is that they are the maximally entangled two-qubit
+   set of basis states.  Maximal entanglement means that these states
+   have the strongest non-classical correlations of all possible two-
+   qubit states.  Furthermore, since single-qubit local operations can
+   never increase entanglement, states that are less entangled would
+   impose some constraints on distributed quantum algorithms.  This
+   makes Bell pairs particularly useful as a generic building block for
+   distributed quantum applications.
+
+4.3.  Teleportation
+
+   The observation that we only need to be able to distribute Bell pairs
+   relies on the fact that this enables the distribution of any other
+   arbitrary entangled state.  This can be achieved via quantum state
+   teleportation [Bennett93].  Quantum state teleportation consumes an
+   unknown qubit state that we want to transmit and recreates it at the
+   desired destination.  This does not violate the no-cloning theorem,
+   as the original state is destroyed in the process.
+
+   To achieve this, an entangled pair needs to be distributed between
+   the source and destination before teleportation commences.  The
+   source then entangles the transmission qubit with its end of the pair
+   and performs a readout of the two qubits (the sum of these operations
+   is called a Bell state measurement).  This consumes the Bell pair's
+   entanglement, turning the source and destination qubits into
+   independent states.  The measurement yields two classical bits, which
+   the source sends to the destination over a classical channel.  Based
+   on the value of the received two classical bits, the destination
+   performs one of four possible corrections (called the Pauli
+   corrections) on its end of the pair, which turns it into the unknown
+   qubit state that we wanted to transmit.  This requirement to
+   communicate the measurement readout over a classical channel
+   unfortunately means that entanglement cannot be used to transmit
+   information faster than the speed of light.
+
+   The unknown quantum state that was transmitted was never fed into the
+   network itself.  Therefore, the network needs to only be able to
+   reliably produce Bell pairs between any two nodes in the network.
+   Thus, a key difference between a classical data plane and a quantum
+   data plane is that a classical data plane carries user data but a
+   quantum data plane provides the resources for the user to transmit
+   user data themselves without further involvement of the network.
+
+4.4.  The Life Cycle of Entanglement
+
+   Reducing the problem of quantum connectivity to one of generating a
+   Bell pair has reduced the problem to a simpler, more fundamental
+   case, but it has not solved it.  In this section, we discuss how
+   these entangled pairs are generated in the first place and how their
+   two qubits are delivered to the end-points.
+
+4.4.1.  Elementary Link Generation
+
+   In a quantum network, entanglement is always first generated locally
+   (at a node or an auxiliary element), followed by a movement of one or
+   both of the entangled qubits across the link through quantum
+   channels.  In this context, photons (particles of light) are the
+   natural candidate for entanglement carriers.  Because these photons
+   carry quantum states from place to place at high speed, we call them
+   flying qubits.  The rationale for this choice is related to the
+   advantages provided by photons, such as moderate interaction with the
+   environment leading to moderate decoherence; convenient control with
+   standard optical components; and high-speed, low-loss transmissions.
+   However, since photons are hard to store, a transducer must transfer
+   the flying qubit's state to a qubit suitable for information
+   processing and/or storage (often referred to as a matter qubit).
+
+   Since this process may fail, in order to generate and store
+   entanglement efficiently, we must be able to distinguish successful
+   attempts from failures.  Entanglement generation schemes that are
+   able to announce successful generation are called heralded
+   entanglement generation schemes.
+
+   There exist three basic schemes for heralded entanglement generation
+   on a link through coordinated action of the two nodes at the two ends
+   of the link [Cacciapuoti19]:
+
+   "At mid-point":  In this scheme, an entangled photon pair source
+      sitting midway between the two nodes with matter qubits sends an
+      entangled photon through a quantum channel to each of the nodes.
+      There, transducers are invoked to transfer the entanglement from
+      the flying qubits to the matter qubits.  In this scheme, the
+      transducers know if the transfers succeeded and are able to herald
+      successful entanglement generation via a message exchange over the
+      classical channel.
+
+   "At source":  In this scheme, one of the two nodes sends a flying
+      qubit that is entangled with one of its matter qubits.  A
+      transducer at the other end of the link will transfer the
+      entanglement from the flying qubit to one of its matter qubits.
+      Just like in the previous scheme, the transducer knows if its
+      transfer succeeded and is able to herald successful entanglement
+      generation with a classical message sent to the other node.
+
+   "At both end-points":  In this scheme, both nodes send a flying qubit
+      that is entangled with one of their matter qubits.  A detector
+      somewhere in between the nodes performs a joint measurement on the
+      flying qubits, which stochastically projects the remote matter
+      qubits into an entangled quantum state.  The detector knows if the
+      entanglement succeeded and is able to herald successful
+      entanglement generation by sending a message to each node over the
+      classical channel.
+
+   The "mid-point source" scheme is more robust to photon loss, but in
+   the other schemes, the nodes retain greater control over the
+   entangled pair generation.
+
+   Note that whilst photons travel in a particular direction through the
+   quantum channel the resulting entangled pair of qubits does not have
+   a direction associated with it.  Physically, there is no upstream or
+   downstream end of the pair.
+
+4.4.2.  Entanglement Swapping
+
+   The problem with generating entangled pairs directly across a link is
+   that efficiency decreases with channel length.  Beyond a few tens of
+   kilometres in optical fibre or 1000 kilometres in free space (via
+   satellite), the rate is effectively zero, and due to the no-cloning
+   theorem we cannot simply amplify the signal.  The solution is
+   entanglement swapping [Briegel98].
+
+   A Bell pair between any two nodes in the network can be constructed
+   by combining the pairs generated along each individual link on a path
+   between the two end-points.  Each node along the path can consume the
+   two pairs on the two links to which it is connected, in order to
+   produce a new entangled pair between the two remote ends.  This
+   process is known as entanglement swapping.  It can be represented
+   pictorially as follows:
+
+   +---------+      +---------+      +---------+
+   |    A    |      |    B    |      |    C    |
+   |         |------|         |------|         |
+   |      X1~~~~~~~~~~X2   Y1~~~~~~~~~~Y2      |
+   +---------+      +---------+      +---------+
+
+   where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2
+   are the qubits of entangled pair Y.  The entanglement is denoted with
+   ~~.  In the diagram above, nodes A and B share the pair X and nodes B
+   and C share the pair Y, but we want entanglement between A and C.
+
+   To achieve this goal, we simply teleport the qubit X2 using the pair
+   Y.  This requires node B to perform a Bell state measurement on the
+   qubits X2 and Y1 that results in the destruction of the entanglement
+   between Y1 and Y2.  However, X2 is recreated in Y2's place, carrying
+   with it its entanglement with X1.  The end result is shown below:
+
+   +---------+      +---------+      +---------+
+   |    A    |      |    B    |      |    C    |
+   |         |------|         |------|         |
+   |      X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2      |
+   +---------+      +---------+      +---------+
+
+   Depending on the needs of the network and/or application, a final
+   Pauli correction at the recipient node may not be necessary, since
+   the result of this operation is also a Bell pair.  However, the two
+   classical bits that form the readout from the measurement at node B
+   must still be communicated, because they carry information about
+   which of the four Bell pairs was actually produced.  If a correction
+   is not performed, the recipient must be informed which Bell pair was
+   received.
+
+   This process of teleporting Bell pairs using other entangled pairs is
+   called entanglement swapping.  Quantum nodes that create long-
+   distance entangled pairs via entanglement swapping are called quantum
+   repeaters in academic literature [Briegel98].  We will use the same
+   terminology in this document.
+
+4.4.3.  Error Management
+
+4.4.3.1.  Distillation
+
+   Neither the generation of Bell pairs nor the swapping operations are
+   noiseless operations.  Therefore, with each link and each swap, the
+   fidelity of the state degrades.  However, it is possible to create
+   higher-fidelity Bell pair states from two or more lower-fidelity
+   pairs through a process called distillation (sometimes also referred
+   to as purification) [Dur07].
+
+   To distil a quantum state, a second (and sometimes third) quantum
+   state is used as a "test tool" to test a proposition about the first
+   state, e.g., "the parity of the two qubits in the first state is
+   even."  When the test succeeds, confidence in the state is improved,
+   and thus the fidelity is improved.  The test tool states are
+   destroyed in the process, so resource demands increase substantially
+   when distillation is used.  When the test fails, the tested state
+   must also be discarded.  Distillation makes low demands on fidelity
+   and resources compared to QEC, but distributed protocols incur round-
+   trip delays due to classical communication [Bennett96].
+
+4.4.3.2.  Quantum Error Correction (QEC)
+
+   Just like classical error correction, QEC encodes logical qubits
+   using several physical (raw) qubits to protect them from the errors
+   described in Section 4.1.3 [Jiang09] [Fowler10] [Devitt13] [Mural16].
+   Furthermore, similarly to its classical counterpart, QEC can not only
+   correct state errors but also account for lost qubits.  Additionally,
+   if all physical qubits that encode a logical qubit are located at the
+   same node, the correction procedure can be executed locally, even if
+   the logical qubit is entangled with remote qubits.
+
+   Although QEC was originally a scheme proposed to protect a qubit from
+   noise, QEC can also be applied to entanglement distillation.  Such
+   QEC-applied distillation is cost effective but requires a higher base
+   fidelity.
+
+4.4.3.3.  Error Management Schemes
+
+   Quantum networks have been categorised into three "generations" based
+   on the error management scheme they employ [Mural16].  Note that
+   these "generations" are more like categories; they do not necessarily
+   imply a time progression and do not obsolete each other, though the
+   later generations do require technologies that are more advanced.
+   Which generation is used depends on the hardware platform and network
+   design choices.
+
+   Table 2 summarises the generations.
+
+   +===========+================+=======================+=============+
+   |           |     First      |   Second generation   |    Third    |
+   |           |   generation   |                       |  generation |
+   +===========+================+=======================+=============+
+   |    Loss   |    Heralded    | Heralded entanglement |   QEC (no   |
+   | tolerance |  entanglement  |       generation      |  classical  |
+   |           |   generation   |     (bidirectional    | signalling) |
+   |           | (bidirectional | classical signalling) |             |
+   |           |   classical    |                       |             |
+   |           |  signalling)   |                       |             |
+   +-----------+----------------+-----------------------+-------------+
+   +-----------+----------------+-----------------------+-------------+
+   |   Error   |  Entanglement  |      Entanglement     |   QEC (no   |
+   | tolerance |  distillation  |      distillation     |  classical  |
+   |           | (bidirectional |    (unidirectional    | signalling) |
+   |           |   classical    | classical signalling) |             |
+   |           |  signalling)   |  or QEC (no classical |             |
+   |           |                |      signalling)      |             |
+   +-----------+----------------+-----------------------+-------------+
+
+              Table 2: Classical Signalling and Generations
+
+   Generations are defined by the directions of classical signalling
+   required in their distributed protocols for loss tolerance and error
+   tolerance.  Classical signalling carries the classical bits,
+   incurring round-trip delays.  As described in Section 4.4.3.1, these
+   delays affect the performance of quantum networks, especially as the
+   distance between the communicating nodes increases.
+
+   Loss tolerance is about tolerating qubit transmission losses between
+   nodes.  Heralded entanglement generation, as described in
+   Section 4.4.1, confirms the receipt of an entangled qubit using a
+   heralding signal.  A pair of directly connected quantum nodes
+   repeatedly attempt to generate an entangled pair until the heralding
+   signal is received.  As described in Section 4.4.3.2, QEC can be
+   applied to complement lost qubits, eliminating the need for
+   reattempts.  Furthermore, since the correction procedure is composed
+   of local operations, it does not require a heralding signal.
+   However, it is possible only when the photon loss rate from
+   transmission to measurement is less than 50%.
+
+   Error tolerance is about tolerating quantum state errors.
+   Entanglement distillation is the easiest mechanism to implement for
+   improved error tolerance, but it incurs round-trip delays due to the
+   requirement for bidirectional classical signalling.  The alternative,
+   QEC, is able to correct state errors locally so that it does not need
+   any classical signalling between the quantum nodes.  In between these
+   two extremes, there is also QEC-applied distillation, which requires
+   unidirectional classical signalling.
+
+   The three "generations" summarised:
+
+   1.  First-generation quantum networks use heralding for loss
+       tolerance and entanglement distillation for error tolerance.
+       These networks can be implemented even with a limited set of
+       available quantum gates.
+
+   2.  Second-generation quantum networks improve upon the first
+       generation with QEC codes for error tolerance (but not loss
+       tolerance).  At first, QEC will be applied to entanglement
+       distillation only, which requires unidirectional classical
+       signalling.  Later, QEC codes will be used to create logical Bell
+       pairs that no longer require any classical signalling for the
+       purposes of error tolerance.  Heralding is still used to
+       compensate for transmission losses.
+
+   3.  Third-generation quantum networks directly transmit QEC-encoded
+       qubits to adjacent nodes, as discussed in Section 4.1.4.
+       Elementary link Bell pairs can now be created without heralding
+       or any other classical signalling.  Furthermore, this also
+       enables direct transmission architectures in which qubits are
+       forwarded end to end like classical packets rather than relying
+       on Bell pairs and entanglement swapping.
+
+   Despite the fact that there are important distinctions in how errors
+   will be managed in the different generations, it is unlikely that all
+   quantum networks will consistently use the same method.  This is due
+   to different hardware requirements of the different generations and
+   the practical reality of network upgrades.  Therefore, it is
+   unavoidable that eventually boundaries between different error
+   management schemes start forming.  This will affect the content and
+   semantics of messages that must cross those boundaries -- for both
+   connection setup and real-time operation [Nagayama16].
+
+4.4.4.  Delivery
+
+   Eventually, the Bell pairs must be delivered to an application (or
+   higher-layer protocol) at the two end nodes.  A detailed list of such
+   requirements is beyond the scope of this document.  At minimum, the
+   end nodes require information to map a particular Bell pair to the
+   qubit in their local memory that is part of this entangled pair.
+
+5.  Architecture of a Quantum Internet
+
+   It is evident from the previous sections that the fundamental service
+   provided by a quantum network significantly differs from that of a
+   classical network.  Therefore, it is not surprising that the
+   architecture of a quantum internet will itself be very different from
+   that of the classical Internet.
+
+5.1.  Challenges
+
+   This subsection covers the major fundamental challenges involved in
+   building quantum networks.  Here, we only describe the fundamental
+   differences.  Technological limitations are described in Section 5.4.
+
+   1.  Bell pairs are not equivalent to packets that carry payload.
+
+       In most classical networks, including Ethernet, Internet Protocol
+       (IP), and Multi-Protocol Label Switching (MPLS) networks, user
+       data is grouped into packets.  In addition to the user data, each
+       packet also contains a series of headers that contain the control
+       information that lets routers and switches forward it towards its
+       destination.  Packets are the fundamental unit in a classical
+       network.
+
+       In a quantum network, the entangled pairs of qubits are the basic
+       unit of networking.  These qubits themselves do not carry any
+       headers.  Therefore, quantum networks will have to send all
+       control information via separate classical channels, which the
+       repeaters will have to correlate with the qubits stored in their
+       memory.  Furthermore, unlike a classical packet, which is located
+       at a single node, a Bell pair consists of two qubits distributed
+       across two nodes.  This has a fundamental impact on how quantum
+       networks will be managed and how protocols need to be designed.
+       To make long-distance Bell pairs, the nodes may have to keep
+       their qubits in their quantum memories and wait until control
+       information is exchanged before proceeding with the next
+       operation.  This signalling will result in additional latency,
+       which will depend on the distance between the nodes holding the
+       two ends of the Bell pair.  Error management, such as
+       entanglement distillation, is a typical example of such control
+       information exchange [Nagayama21] (see also Section 4.4.3.3).
+
+   2.  "Store and forward" and "store and swap" quantum networks require
+       different state management techniques.
+
+       As described in Section 4.4.1, quantum links provide Bell pairs
+       that are undirected network resources, in contrast to directed
+       frames of classical networks.  This phenomenological distinction
+       leads to architectural differences between quantum networks and
+       classical networks.  Quantum networks combine multiple elementary
+       link Bell pairs together to create one end-to-end Bell pair,
+       whereas classical networks deliver messages from one end to the
+       other end hop by hop.
+
+       Classical networks receive data on one interface, store it in
+       local buffers, and then forward the data to another appropriate
+       interface.  Quantum networks store Bell pairs and then execute
+       entanglement swapping instead of forwarding in the data plane.
+       Such quantum networks are "store and swap" networks.  In "store
+       and swap" networks, we do not need to care about the order in
+       which the Bell pairs were generated, since they are undirected.
+       However, whilst the ordering does not matter, it is very
+       important that the right entangled pairs get swapped, and that
+       the intermediate measurement outcomes (see Section 4.4.2) are
+       signalled to and correlated with the correct qubits at the other
+       nodes.  Otherwise, the final end-to-end entangled pair will not
+       be created between the expected end-points or will be in a
+       different quantum state than expected.  For example, rather than
+       Alice receiving a qubit that is entangled with Bob's qubit, her
+       qubit is entangled with Charlie's qubit.  This distinction makes
+       control algorithms and optimisation of quantum networks different
+       from those for classical networks, in the sense that swapping is
+       stateful in contrast to stateless packet-by-packet forwarding.
+       Note that, as described in Section 4.4.3.3, third-generation
+       quantum networks will be able to support a "store and forward"
+       architecture in addition to "store and swap".
+
+   3.  An entangled pair is only useful if the locations of both qubits
+       are known.
+
+       A classical network packet logically exists only at one location
+       at any point in time.  If a packet is modified in some way,
+       whether headers or payload, this information does not need to be
+       conveyed to anybody else in the network.  The packet can be
+       simply forwarded as before.
+
+       In contrast, entanglement is a phenomenon in which two or more
+       qubits exist in a physically distributed state.  Operations on
+       one of the qubits change the mutual state of the pair.  Since the
+       owner of a particular qubit cannot just read out its state, it
+       must coordinate all its actions with the owner of the pair's
+       other qubit.  Therefore, the owner of any qubit that is part of
+       an entangled pair must know the location of its counterpart.
+       Location, in this context, need not be the explicit spatial
+       location.  A relevant pair identifier, a means of communication
+       between the pair owners, and an association between the pair ID
+       and the individual qubits will be sufficient.
+
+   4.  Generating entanglement requires temporary state.
+
+       Packet forwarding in a classical network is largely a stateless
+       operation.  When a packet is received, the router does a lookup
+       in its forwarding table and sends the packet out of the
+       appropriate output.  There is no need to keep any memory of the
+       packet any more.
+
+       A quantum node must be able to make decisions about qubits that
+       it receives and is holding in its memory.  Since qubits do not
+       carry headers, the receipt of an entangled pair conveys no
+       control information based on which the repeater can make a
+       decision.  The relevant control information will arrive
+       separately over a classical channel.  This implies that a
+       repeater must store temporary state, as the control information
+       and the qubit it pertains to will, in general, not arrive at the
+       same time.
+
+5.2.  Classical Communication
+
+   In this document, we have already covered two different roles that
+   classical communication must perform the following:
+
+   *  Communicate classical bits of information as part of distributed
+      protocols such as entanglement swapping and teleportation.
+
+   *  Communicate control information within a network, including
+      background protocols such as routing, as well as signalling
+      protocols to set up end-to-end entanglement generation.
+
+   Classical communication is a crucial building block of any quantum
+   network.  All nodes in a quantum network are assumed to have
+   classical connectivity with each other (within typical administrative
+   domain limits).  Therefore, quantum nodes will need to manage two
+   data planes in parallel: a classical data plane and a quantum data
+   plane.  Additionally, a node must be able to correlate information
+   between the two planes so that the control information received on a
+   classical channel can be applied to the qubits managed by the quantum
+   data plane.
+
+5.3.  Abstract Model of the Network
+
+5.3.1.  The Control Plane and the Data Plane
+
+   Control plane protocols for quantum networks will have many
+   responsibilities similar to their classical counterparts, namely
+   discovering the network topology, resource management, populating
+   data plane tables, etc.  Most of these protocols do not require the
+   manipulation of quantum data and can operate simply by exchanging
+   classical messages only.  There may also be some control plane
+   functionality that does require the handling of quantum data
+   [QI-Scenarios].  As it is not clear if there is much benefit in
+   defining a separate quantum control plane given the significant
+   overlap in responsibilities with its classical counterpart, the
+   question of whether there should be a separate quantum control plane
+   is beyond the scope of this document.
+
+   However, the data plane separation is much more distinct, and there
+   will be two data planes: a classical data plane and a quantum data
+   plane.  The classical data plane processes and forwards classical
+   packets.  The quantum data plane processes and swaps entangled pairs.
+   Third-generation quantum networks may also forward qubits in addition
+   to swapping Bell pairs.
+
+   In addition to control plane messages, there will also be control
+   information messages that operate at the granularity of individual
+   entangled pairs, such as heralding messages used for elementary link
+   generation (Section 4.4.1).  In terms of functionality, these
+   messages are closer to classical packet headers than control plane
+   messages, and thus we consider them to be part of the quantum data
+   plane.  Therefore, a quantum data plane also includes the exchange of
+   classical control information at the granularity of individual qubits
+   and entangled pairs.
+
+5.3.2.  Elements of a Quantum Network
+
+   We have identified quantum repeaters as the core building block of a
+   quantum network.  However, a quantum repeater will have to do more
+   than just entanglement swapping in a functional quantum network.  Its
+   key responsibilities will include the following:
+
+   1.  Creating link-local entanglement between neighbouring nodes.
+
+   2.  Extending entanglement from link-local pairs to long-range pairs
+       through entanglement swapping.
+
+   3.  Performing distillation to manage the fidelity of the produced
+       pairs.
+
+   4.  Participating in the management of the network (routing, etc.).
+
+   Not all quantum repeaters in the network will be the same; here, we
+   break them down further:
+
+   Quantum routers (controllable quantum nodes):  A quantum router is a
+      quantum repeater with a control plane that participates in the
+      management of the network and will make decisions about which
+      qubits to swap to generate the requested end-to-end pairs.
+
+   Automated quantum nodes:  An automated quantum node is a data-plane-
+      only quantum repeater that does not participate in the network
+      control plane.  Since the no-cloning theorem precludes the use of
+      amplification, long-range links will be established by chaining
+      multiple such automated nodes together.
+
+   End nodes:  End nodes in a quantum network must be able to receive
+      and handle an entangled pair, but they do not need to be able to
+      perform an entanglement swap (and thus are not necessarily quantum
+      repeaters).  End nodes are also not required to have any quantum
+      memory, as certain quantum applications can be realised by having
+      the end node measure its qubit as soon as it is received.
+
+   Non-quantum nodes:  Not all nodes in a quantum network need to have a
+      quantum data plane.  A non-quantum node is any device that can
+      handle classical network traffic.
+
+   Additionally, we need to identify two kinds of links that will be
+   used in a quantum network:
+
+   Quantum links:  A quantum link is a link that can be used to generate
+      an entangled pair between two directly connected quantum
+      repeaters.  This may include additional mid-point elements as
+      described in Section 4.4.1.  It may also include a dedicated
+      classical channel that is to be used solely for the purpose of
+      coordinating the entanglement generation on this quantum link.
+
+   Classical links:  A classical link is a link between any node in the
+      network that is capable of carrying classical network traffic.
+
+   Note that passive elements, such as optical switches, do not destroy
+   the quantum state.  Therefore, it is possible to connect multiple
+   quantum nodes with each other over an optical network and perform
+   optical switching rather than routing via entanglement swapping at
+   quantum routers.  This does require coordination with the elementary
+   link entanglement generation process, and it still requires repeaters
+   to overcome the short-distance limitations.  However, this is a
+   potentially feasible architecture for local area networks.
+
+5.3.3.  Putting It All Together
+
+   A two-hop path in a generic quantum network can be represented as
+   follows:
+
+   +-----+                                        +-----+
+   | App |- - - - - - - - - -CC- - - - - - - - - -| App |
+   +-----+                +------+                +-----+
+   | EN  |------ CL ------|  QR  |------ CL ------| EN  |
+   |     |------ QL ------|      |------ QL ------|     |
+   +-----+                +------+                +-----+
+
+   App - user-level application
+   EN - End Node
+   QL - Quantum Link
+   CL - Classical Link
+   CC - Classical Channel (traverses one or more CLs)
+   QR - Quantum Repeater
+
+   An application (App) running on two End Nodes (ENs) attached to a
+   network will at some point need the network to generate entangled
+   pairs for its use.  This may require negotiation between the ENs
+   (possibly ahead of time), because they must both open a communication
+   end-point that the network can use to identify the two ends of the
+   connection.  The two ENs use a Classical Channel (CC) available in
+   the network to achieve this goal.
+
+   When the network receives a request to generate end-to-end entangled
+   pairs, it uses the Classical Links (CLs) to coordinate and claim the
+   resources necessary to fulfill this request.  This may be some
+   combination of prior control information (e.g., routing tables) and
+   signalling protocols, but the details of how this is achieved are an
+   active research question.  A thought experiment on what this might
+   look like be can be found in Section 7.
+
+   During or after the distribution of control information, the network
+   performs the necessary quantum operations, such as generating
+   entanglement over individual Quantum Links (QLs), performing
+   entanglement swaps at Quantum Repeaters (QRs), and further signalling
+   to transmit the swap outcomes and other control information.  Since
+   Bell pairs do not carry any user data, some of these operations can
+   be performed before the request is received, in anticipation of the
+   demand.
+
+   Note that here, "signalling" is used in a very broad sense and covers
+   many different types of messaging necessary for entanglement
+   generation control.  For example, heralded entanglement generation
+   requires very precise timing synchronisation between the neighbouring
+   nodes, and thus the triggering of entanglement generation and
+   heralding may happen over its own, perhaps physically separate, CL,
+   as was the case in the network stack demonstration described in
+   [Pompili21.2].  Higher-level signalling with timing requirements that
+   are less stringent (e.g., control plane signalling) may then happen
+   over its own CL.
+
+   The entangled pair is delivered to the application once it is ready,
+   together with the relevant pair identifier.  However, being ready
+   does not necessarily mean that all link pairs and entanglement swaps
+   are complete, as some applications can start executing on an
+   incomplete pair.  In this case, the remaining entanglement swaps will
+   propagate the actions across the network to the other end, sometimes
+   necessitating fixup operations at the EN.
+
+5.4.  Physical Constraints
+
+   The model above has effectively abstracted away the particulars of
+   the hardware implementation.  However, certain physical constraints
+   need to be considered in order to build a practical network.  Some of
+   these are fundamental constraints, and no matter how much the
+   technology improves, they will always need to be addressed.  Others
+   are artifacts of the early stages of a new technology.  Here, we
+   consider a highly abstract scenario and refer to [Wehner18] for
+   pointers to the physics literature.
+
+5.4.1.  Memory Lifetimes
+
+   In addition to discrete operations being imperfect, storing a qubit
+   in memory is also highly non-trivial.  The main difficulty in
+   achieving persistent storage is that it is extremely challenging to
+   isolate a quantum system from the environment.  The environment
+   introduces an uncontrollable source of noise into the system, which
+   affects the fidelity of the state.  This process is known as
+   decoherence.  Eventually, the state has to be discarded once its
+   fidelity degrades too much.
+
+   The memory lifetime depends on the particular physical setup, but the
+   highest achievable values in quantum network hardware are, as of
+   2020, on the order of seconds [Abobeih18], although a lifetime of a
+   minute has also been demonstrated for qubits not connected to a
+   quantum network [Bradley19].  These values have increased
+   tremendously over the lifetime of the different technologies and are
+   bound to keep increasing.  However, if quantum networks are to be
+   realised in the near future, they need to be able to handle short
+   memory lifetimes -- for example, by reducing latency on critical
+   paths.
+
+5.4.2.  Rates
+
+   Entanglement generation on a link between two connected nodes is not
+   a very efficient process, and it requires many attempts to succeed
+   [Hensen15] [Dahlberg19].  For example, the highest achievable rates
+   of success between nitrogen-vacancy center nodes -- which, in
+   addition to entanglement generation are also capable of storing and
+   processing the resulting qubits -- are on the order of 10 Hz.
+   Combined with short memory lifetimes, this leads to very tight timing
+   windows to build up network-wide connectivity.
+
+   Other platforms have shown higher entanglement rates, but this
+   usually comes at the cost of other hardware capabilities, such as no
+   quantum memory and/or limited processing capabilities [Wei22].
+   Nevertheless, the current rates are not sufficient for practical
+   applications beyond simple experimental proofs of concept.  However,
+   they are expected to improve over time as quantum network technology
+   evolves [Wei22].
+
+5.4.3.  Communication Qubits
+
+   Most physical architectures capable of storing qubits are only able
+   to generate entanglement using only a subset of available qubits
+   called communication qubits [Dahlberg19].  Once a Bell pair has been
+   generated using a communication qubit, its state can be transferred
+   into memory.  This may impose additional limitations on the network.
+   In particular, if a given node has only one communication qubit, it
+   cannot simultaneously generate Bell pairs over two links.  It must
+   generate entanglement over the links one at a time.
+
+5.4.4.  Homogeneity
+
+   At present, all existing quantum network implementations are
+   homogeneous, and they do not interface with each other.  In general,
+   it is very challenging to combine different quantum information
+   processing technologies.
+
+   There are many different physical hardware platforms for implementing
+   quantum networking hardware.  The different technologies differ in
+   how they store and manipulate qubits in memory and how they generate
+   entanglement across a link with their neighbours.  For example,
+   hardware based on optical elements and atomic ensembles [Sangouard11]
+   is very efficient at generating entanglement at high rates but
+   provides limited processing capabilities once the entanglement is
+   generated.  On the other hand, nitrogen-vacancy-based platforms
+   [Hensen15] or trapped ion platforms [Moehring07] offer a much greater
+   degree of control over the qubits but have a harder time generating
+   entanglement at high rates.
+
+   In order to overcome the weaknesses of the different platforms,
+   coupling the different technologies will help to build fully
+   functional networks.  For example, end nodes may be implemented using
+   technology with good qubit processing capabilities to enable complex
+   applications, but automated quantum nodes that serve only to "repeat"
+   along a linear chain, where the processing logic is much simpler, can
+   be implemented with technologies that sacrifice processing
+   capabilities for higher entanglement rates at long distances
+   [Askarani21].
+
+   This point is further exacerbated by the fact that quantum computers
+   (i.e., end nodes in a quantum network) are often based on different
+   hardware platforms than quantum repeaters, thus requiring a coupling
+   (transduction) between the two.  This is especially true for quantum
+   computers based on superconducting technology, which are challenging
+   to connect to optical networks.  However, even trapped ion quantum
+   computers, which make up a platform that has shown promise for
+   quantum networking, will still need to connect to other platforms
+   that are better at creating entanglement at high rates over long
+   distances (hundreds of kilometres).
+
+6.  Architectural Principles
+
+   Given that the most practical way of realising quantum network
+   connectivity is using Bell pair and entanglement-swapping repeater
+   technology, what sort of principles should guide us in assembling
+   such networks such that they are functional, robust, efficient, and,
+   most importantly, will work?  Furthermore, how do we design networks
+   so that they work under the constraints imposed by the hardware
+   available today but do not impose unnecessary burdens on future
+   technology?
+
+   As quantum networking is a completely new technology that is likely
+   to see many iterations over its lifetime, this document must not
+   serve as a definitive set of rules but merely as a general set of
+   recommended guidelines for the first generations of quantum networks
+   based on principles and observations made by the community.  The
+   benefit of having a community-built document at this early stage is
+   that expertise in both quantum information and network architecture
+   is needed in order to successfully build a quantum internet.
+
+6.1.  Goals of a Quantum Internet
+
+   When outlining any set of principles, we must ask ourselves what
+   goals we want to achieve, as inevitably trade-offs must be made.  So,
+   what sort of goals should drive a quantum network architecture?  The
+   following list has been inspired by the history of computer
+   networking, and thus it is inevitably very similar to one that could
+   be produced for the classical Internet [Clark88].  However, whilst
+   the goals may be similar, the challenges involved are often
+   fundamentally different.  The list will also most likely evolve with
+   time and the needs of its users.
+
+   1.  Support distributed quantum applications.
+
+       This goal seems trivially obvious, but it makes a subtle, but
+       important, point that highlights a key difference between quantum
+       and classical networks.  Ultimately, quantum data transmission is
+       not the goal of a quantum network -- it is only one possible
+       component of quantum application protocols that are more advanced
+       [Wehner18].  Whilst transmission certainly could be used as a
+       building block for all quantum applications, it is not the most
+       basic one possible.  For example, entanglement-based QKD, the
+       most well-known quantum application protocol, only relies on the
+       stronger-than-classical correlations and inherent secrecy of
+       entangled Bell pairs and does not have to transmit arbitrary
+       quantum states [Ekert91].
+
+       The primary purpose of a quantum internet is to support
+       distributed quantum application protocols, and it is of utmost
+       importance that they can run well and efficiently.  Thus, it is
+       important to develop performance metrics meaningful to
+       applications to drive the development of quantum network
+       protocols.  For example, the Bell pair generation rate is
+       meaningless if one does not also consider their fidelity.  It is
+       generally much easier to generate pairs of lower fidelity, but
+       quantum applications may have to make multiple reattempts or even
+       abort if the fidelity is too low.  A review of the requirements
+       for different known quantum applications can be found in
+       [Wehner18], and an overview of use cases can be found in
+       [QI-Scenarios].
+
+   2.  Support tomorrow's distributed quantum applications.
+
+       The only principle of the Internet that should survive
+       indefinitely is the principle of constant change [RFC1958].
+       Technical change is continuous, and the size and capabilities of
+       the quantum internet will change by orders of magnitude.
+       Therefore, it is an explicit goal that a quantum internet
+       architecture be able to embrace this change.  We have the benefit
+       of having been witness to the evolution of the classical Internet
+       over several decades, and we have seen what worked and what did
+       not.  It is vital for a quantum internet to avoid the need for
+       flag days (e.g., NCP to TCP/IP) or upgrades that take decades to
+       roll out (e.g., IPv4 to IPv6).
+
+       Therefore, it is important that any proposed architecture for
+       general-purpose quantum repeater networks can integrate new
+       devices and solutions as they become available.  The architecture
+       should not be constrained due to considerations for early-stage
+       hardware and applications.  For example, it is already possible
+       to run QKD efficiently on metropolitan-scale networks, and such
+       networks are already commercially available.  However, they are
+       not based on quantum repeaters and thus will not be able to
+       easily transition to applications that are more sophisticated.
+
+   3.  Support heterogeneity.
+
+       There are multiple proposals for realising practical quantum
+       repeater hardware, and they all have their advantages and
+       disadvantages.  Some may offer higher Bell pair generation rates
+       on individual links at the cost of entanglement swap operations
+       that are more difficult.  Other platforms may be good all around
+       but are more difficult to build.
+
+       In addition to physical boundaries, there may be distinctions in
+       how errors are managed (Section 4.4.3.3).  These differences will
+       affect the content and semantics of messages that cross these
+       boundaries -- for both connection setup and real-time operation.
+
+       The optimal network configuration will likely leverage the
+       advantages of multiple platforms to optimise the provided
+       service.  Therefore, it is an explicit goal to incorporate varied
+       hardware and technology support from the beginning.
+
+   4.  Ensure security at the network level.
+
+       The question of security in quantum networks is just as critical
+       as it is in the classical Internet, especially since enhanced
+       security offered by quantum entanglement is one of the key
+       driving factors.
+
+       Fortunately, from an application's point of view, as long as the
+       underlying implementation corresponds to (or sufficiently
+       approximates) theoretical models of quantum cryptography, quantum
+       cryptographic protocols do not need the network to provide any
+       guarantees about the confidentiality or integrity of the
+       transmitted qubits or the generated entanglement (though they may
+       impose requirements on the classical channel, e.g., to be
+       authenticated [Wang21]).  Instead, applications will leverage the
+       classical networks to establish the end-to-end security of the
+       results obtained from the processing of entangled qubits.
+       However, it is important to note that whilst classical networks
+       are necessary to establish these end-to-end guarantees, the
+       security relies on the properties of quantum entanglement.  For
+       example, QKD uses classical information reconciliation [Tang19]
+       for error correction and privacy amplification [Elkouss11] for
+       generating the final secure key, but the raw bits that are fed
+       into these protocols must come from measuring entangled qubits
+       [Ekert91].  In another application, secure delegated quantum
+       computing, the client hides its computation from the server by
+       sending qubits to the server and then requesting (in a classical
+       message) that the server measure them in an encoded basis.  The
+       client then decodes the results it receives from the server to
+       obtain the result of the computation [Broadbent10].  Once again,
+       whilst a classical network is used to achieve the goal of secure
+       computation, the remote computation is strictly quantum.
+
+       Nevertheless, whilst applications can ensure their own end-to-end
+       security, network protocols themselves should be security aware
+       in order to protect the network itself and limit disruption.
+       Whilst the applications remain secure, they are not necessarily
+       operational or as efficient in the presence of an attacker.  For
+       example, if an attacker can measure every qubit between two
+       parties trying to establish a key using QKD, no secret key can be
+       generated.  Security concerns in quantum networks are described
+       in more detail in [Satoh17] and [Satoh20].
+
+   5.  Make them easy to monitor.
+
+       In order to manage, evaluate the performance of, or debug a
+       network, it is necessary to have the ability to monitor the
+       network while ensuring that there will be mechanisms in place to
+       protect the confidentiality and integrity of the devices
+       connected to it.  Quantum networks bring new challenges in this
+       area, so it should be a goal of a quantum network architecture to
+       make this task easy.
+
+       The fundamental unit of quantum information, the qubit, cannot be
+       actively monitored, as any readout irreversibly destroys its
+       contents.  One of the implications of this fact is that measuring
+       an individual pair's fidelity is impossible.  Fidelity is
+       meaningful only as a statistical quantity that requires constant
+       monitoring of generated Bell pairs, achieved by sacrificing some
+       Bell pairs for use in tomography or other methods.
+
+       Furthermore, given one end of an entangled pair, it is impossible
+       to tell where the other qubit is without any additional classical
+       metadata.  It is impossible to extract this information from the
+       qubits themselves.  This implies that tracking entangled pairs
+       necessitates some exchange of classical information.  This
+       information might include (i) a reference to the entangled pair
+       that allows distributed applications to coordinate actions on
+       qubits of the same pair and (ii) the two bits from each
+       entanglement swap necessary to identify the final state of the
+       Bell pair (Section 4.4.2).
+
+   6.  Ensure availability and resilience.
+
+       Any practical and usable network, classical or quantum, must be
+       able to continue to operate despite losses and failures and be
+       robust to malicious actors trying to disable connectivity.  A
+       difference between quantum and classical networks is that quantum
+       networks are composed of two types of data planes (quantum and
+       classical) and two types of channels (quantum and classical) that
+       must be considered.  Therefore, availability and resilience will
+       most likely require a more advanced treatment than they do in
+       classical networks.
+
+   Note that privacy, whilst related to security, is not listed as an
+   explicit goal, because the privacy benefits will depend on the use
+   case.  For example, QKD only provides increased security for the
+   distribution of symmetric keys [Bennett14] [Ekert91].  The handling,
+   manipulation, sharing, encryption, and decryption of data will remain
+   entirely classical, limiting the benefits to privacy that can be
+   gained from using a quantum network.  On the other hand, there are
+   applications like blind quantum computation, which provides the user
+   with the ability to execute a quantum computation on a remote server
+   without the server knowing what the computation was or its input and
+   output [Fitzsimons17].  Therefore, privacy must be considered on a
+   per-application basis.  An overview of quantum network use cases can
+   be found in [QI-Scenarios].
+
+6.2.  The Principles of a Quantum Internet
+
+   The principles support the goals but are not goals themselves.  The
+   goals define what we want to build, and the principles provide a
+   guideline for how we might achieve this.  The goals will also be the
+   foundation for defining any metric of success for a network
+   architecture, whereas the principles in themselves do not distinguish
+   between success and failure.  For more information about design
+   considerations for quantum networks, see [VanMeter13.1] and
+   [Dahlberg19].
+
+   1.  Entanglement is the fundamental service.
+
+       The key service that a quantum network provides is the
+       distribution of entanglement between the nodes in a network.  All
+       distributed quantum applications are built on top of this key
+       resource.  Applications such as clustered quantum computing,
+       distributed quantum computing, distributed quantum sensing
+       networks, and certain kinds of quantum secure networks all
+       consume quantum entanglement as a resource.  Some applications
+       (e.g., QKD) simply measure the entangled qubits to obtain a
+       shared secret key [QKD].  Other applications (e.g., distributed
+       quantum computing) build abstractions and operations that are
+       more complex on the entangled qubits, e.g., distributed CNOT
+       gates [DistCNOT] or teleportation of arbitrary qubit states
+       [Teleportation].
+
+       A quantum network may also distribute multipartite entangled
+       states (entangled states of three or more qubits) [Meignant19],
+       which are useful for applications such as conference key
+       agreement [Murta20], distributed quantum computing [Cirac99],
+       secret sharing [Qin17], and clock synchronisation [Komar14],
+       though it is worth noting that multipartite entangled states can
+       also be constructed from multiple entangled pairs distributed
+       between the end nodes.
+
+   2.  Bell pairs are indistinguishable.
+
+       Any two Bell pairs between the same two nodes are
+       indistinguishable for the purposes of an application, provided
+       they both satisfy its required fidelity threshold.  This
+       observation is likely to be key in enabling a more optimal
+       allocation of resources in a network, e.g., for the purposes of
+       provisioning resources to meet application demand.  However, the
+       qubits that make up the pair themselves are not
+       indistinguishable, and the two nodes operating on a pair must
+       coordinate to make sure they are operating on qubits that belong
+       to the same Bell pair.
+
+   3.  Fidelity is part of the service.
+
+       In addition to being able to deliver Bell pairs to the
+       communication end-points, the Bell pairs must be of sufficient
+       fidelity.  Unlike in classical networks, where most errors are
+       effectively eliminated before reaching the application, many
+       quantum applications only need imperfect entanglement to
+       function.  However, quantum applications will generally have a
+       threshold for Bell pair fidelity below which they are no longer
+       able to operate.  Different applications will have different
+       requirements for what fidelity they can work with.  It is the
+       network's responsibility to balance the resource usage with
+       respect to the applications' requirements.  It may be that it is
+       cheaper for the network to provide lower-fidelity pairs that are
+       just above the threshold required by the application than it is
+       to guarantee high-fidelity pairs to all applications regardless
+       of their requirements.
+
+   4.  Time is an expensive resource.
+
+       Time is not the only resource that is in short supply
+       (communication qubits and memory are as well), but ultimately it
+       is the lifetime of quantum memories that imposes some of the most
+       difficult conditions for operating an extended network of quantum
+       nodes.  Current hardware has low rates of Bell pair generation,
+       short memory lifetimes, and access to a limited number of
+       communication qubits.  All these factors combined mean that even
+       a short waiting queue at some node could be enough for a Bell
+       pair to decohere or result in an end-to-end pair below an
+       application's fidelity threshold.  Therefore, managing the idle
+       time of qubits holding live quantum states should be done
+       carefully -- ideally by minimising the idle time, but potentially
+       also by moving the quantum state for temporary storage to a
+       quantum memory with a longer lifetime.
+
+   5.  Be flexible with regards to capabilities and limitations.
+
+       This goal encompasses two important points:
+
+       *  First, the architecture should be able to function under the
+          physical constraints imposed by the current-generation
+          hardware.  Near-future hardware will have low entanglement
+          generation rates, quantum memories able to hold a handful of
+          qubits at best, and decoherence rates that will render many
+          generated pairs unusable.
+
+       *  Second, the architecture should not make it difficult to run
+          the network over any hardware that may come along in the
+          future.  The physical capabilities of repeaters will improve,
+          and redeploying a technology is extremely challenging.
+
+7.  A Thought Experiment Inspired by Classical Networks
+
+   To conclude, we discuss a plausible quantum network architecture
+   inspired by MPLS.  This is not an architecture proposal but rather a
+   thought experiment to give the reader an idea of what components are
+   necessary for a functional quantum network.  We use classical MPLS as
+   a basis, as it is well known and understood in the networking
+   community.
+
+   Creating end-to-end Bell pairs between remote end-points is a
+   stateful distributed task that requires a lot of a priori
+   coordination.  Therefore, a connection-oriented approach seems the
+   most natural for quantum networks.  In connection-oriented quantum
+   networks, when two quantum application end-points wish to start
+   creating end-to-end Bell pairs, they must first create a Quantum
+   Virtual Circuit (QVC).  As an analogy, in MPLS networks, end-points
+   must establish a Label Switched Path (LSP) before exchanging traffic.
+   Connection-oriented quantum networks may also support virtual
+   circuits with multiple end-points for creating multipartite
+   entanglement.  As an analogy, MPLS networks have the concept of
+   multipoint LSPs for multicast.
+
+   When a quantum application creates a QVC, it can indicate Quality of
+   Service (QoS) parameters such as the required capacity in end-to-end
+   Bell Pairs Per Second (BPPS) and the required fidelity of the Bell
+   pairs.  As an analogy, in MPLS networks, applications specify the
+   required bandwidth in Bits Per Second (BPS) and other constraints
+   when they create a new LSP.
+
+   Different applications will have different QoS requirements.  For
+   example, applications such as QKD that don't need to process the
+   entangled qubits, and only need measure them and store the resulting
+   outcome, may require a large volume of entanglement but will be
+   tolerant of delay and jitter for individual pairs.  On the other
+   hand, distributed/cloud quantum computing applications may need fewer
+   entangled pairs but instead may need all of them to be generated in
+   one go so that they can all be processed together before any of them
+   decohere.
+
+   Quantum networks need a routing function to compute the optimal path
+   (i.e., the best sequence of routers and links) for each new QVC.  The
+   routing function may be centralised or distributed.  In the latter
+   case, the quantum network needs a distributed routing protocol.  As
+   an analogy, classical networks use routing protocols such as Open
+   Shortest Path First (OSPF) and Intermediate System to Intermediate
+   System (IS-IS).  However, note that the definition of "shortest path"
+   / "least cost" may be different in a quantum network to account for
+   its non-classical features, such as fidelity [VanMeter13.2].
+
+   Given the very scarce availability of resources in early quantum
+   networks, a Traffic Engineering (TE) function is likely to be
+   beneficial.  Without TE, QVCs always use the shortest path.  In this
+   case, the quantum network cannot guarantee that each quantum end-
+   point will get its Bell pairs at the required rate or fidelity.  This
+   is analogous to "best effort" service in classical networks.
+
+   With TE, QVCs choose a path that is guaranteed to have the requested
+   resources (e.g., bandwidth in BPPS) available, taking into account
+   the capacity of the routers and links and also taking into account
+   the resources already consumed by other virtual circuits.  As an
+   analogy, both OSPF and IS-IS have TE extensions to keep track of used
+   and available resources and can use Constrained Shortest Path First
+   (CSPF) to take resource availability and other constraints into
+   account when computing the optimal path.
+
+   The use of TE implies the use of Call Admission Control (CAC): the
+   network denies any virtual circuits for which it cannot guarantee the
+   requested quality of service a priori.  Alternatively, the network
+   preempts lower-priority circuits to make room for a new circuit.
+
+   Quantum networks need a signalling function: once the path for a QVC
+   has been computed, signalling is used to install the "forwarding
+   rules" into the data plane of each quantum router on the path.  The
+   signalling may be distributed, analogous to the Resource Reservation
+   Protocol (RSVP) in MPLS.  Or, the signalling may be centralised,
+   similar to OpenFlow.
+
+   Quantum networks need an abstraction of the hardware for specifying
+   the forwarding rules.  This allows us to decouple the control plane
+   (routing and signalling) from the data plane (actual creation of Bell
+   pairs).  The forwarding rules are specified using abstract building
+   blocks such as "creating local Bell pairs", "swapping Bell pairs", or
+   "distillation of Bell pairs".  As an analogy, classical networks use
+   abstractions that are based on match conditions (e.g., looking up
+   header fields in tables) and actions (e.g., modifying fields or
+   forwarding a packet to a specific interface).  The data plane
+   abstractions in quantum networks will be very different from those in
+   classical networks due to the fundamental differences in technology
+   and the stateful nature of quantum networks.  In fact, choosing the
+   right abstractions will be one of the biggest challenges when
+   designing interoperable quantum network protocols.
+
+   In quantum networks, control plane traffic (routing and signalling
+   messages) is exchanged over a classical channel, whereas data plane
+   traffic (the actual Bell pair qubits) is exchanged over a separate
+   quantum channel.  This is in contrast to most classical networks,
+   where control plane traffic and data plane traffic share the same
+   channel and where a single packet contains both user fields and
+   header fields.  There is, however, a classical analogy to the way
+   quantum networks work: generalised MPLS (GMPLS) networks use separate
+   channels for control plane traffic and data plane traffic.
+   Furthermore, GMPLS networks support data planes where there is no
+   such thing as data plane headers (e.g., Dense Wavelength Division
+   Multiplexing (DWDM) or Time-Division Multiplexing (TDM) networks).
+
+8.  Security Considerations
+
+   Security is listed as an explicit goal for the architecture; this
+   issue is addressed in Section 6.1.  However, as this is an
+   Informational document, it does not propose any concrete mechanisms
+   to achieve these goals.
+
+9.  IANA Considerations
+
+   This document has no IANA actions.
+
+10.  Informative References
+
+   [Abobeih18]
+              Abobeih, M.H., Cramer, J., Bakker, M.A., Kalb, N.,
+              Markham, M., Twitchen, D.J., and T.H. Taminiau, "One-
+              second coherence for a single electron spin coupled to a
+              multi-qubit nuclear-spin environment", Nature
+              communications Vol. 9, Iss. 1, pp. 1-8,
+              DOI 10.1038/s41467-018-04916-z, June 2018,
+              <https://www.nature.com/articles/s41467-018-04916-z>.
+
+   [Aguado19] Aguado, A., Lopez, V., Lopez, D., Peev, M., Poppe, A.,
+              Pastor, A., Folgueira, J., and V. Martin, "The Engineering
+              of Software-Defined Quantum Key Distribution Networks",
+              IEEE Communications Magazine Vol. 57, Iss. 7, pp. 20-26,
+              DOI 10.1109/MCOM.2019.1800763, July 2019,
+              <https://ieeexplore.ieee.org/document/8767074>.
+
+   [Askarani21]
+              Askarani, M.F., Chakraborty, K., and G.C. do Amaral,
+              "Entanglement distribution in multi-platform buffered-
+              router-assisted frequency-multiplexed automated repeater
+              chains", New Journal of Physics Vol. 23, Iss. 6, 063078,
+              DOI 10.1088/1367-2630/ac0a35, June 2021,
+              <https://iopscience.iop.org/article/10.1088/1367-2630/
+              ac0a35>.
+
+   [Aspect81] Aspect, A., Grangier, P., and G. Roger, "Experimental
+              Tests of Realistic local Theories via Bell's Theorem",
+              Physical Review Letters Vol. 47, Iss. 7, pp. 460-463,
+              DOI 10.1103/PhysRevLett.47.460, August 1981,
+              <https://journals.aps.org/prl/abstract/10.1103/
+              PhysRevLett.47.460>.
+
+   [Bennett14]
+              Bennett, C.H. and G. Brassard, "Quantum cryptography:
+              Public key distribution and coin tossing", Theoretical
+              Computer Science Vol. 560 (Part 1), pp. 7-11,
+              DOI 10.1016/j.tcs.2014.05.025, December 2014,
+              <https://www.sciencedirect.com/science/article/pii/
+              S0304397514004241?via%3Dihub>.
+
+   [Bennett93]
+              Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R.,
+              Peres, A., and W.K. Wootters, "Teleporting an unknown
+              quantum state via dual classical and Einstein-Podolsky-
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+Acknowledgements
+
+   The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel
+   Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang,
+   Scott Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG
+   community as a whole for their very useful reviews and comments on
+   this document.
+
+   WK and SW acknowledge funding received from the EU Flagship on
+   Quantum Technologies, Quantum Internet Alliance (No. 820445).
+
+   rdv acknowledges support by the Air Force Office of Scientific
+   Research under award number FA2386-19-1-4038.
+
+Authors' Addresses
+
+   Wojciech Kozlowski
+   QuTech
+   Building 22
+   Lorentzweg 1
+   2628 CJ Delft
+   Netherlands
+   Email: w.kozlowski@tudelft.nl
+
+
+   Stephanie Wehner
+   QuTech
+   Building 22
+   Lorentzweg 1
+   2628 CJ Delft
+   Netherlands
+   Email: s.d.c.wehner@tudelft.nl
+
+
+   Rodney Van Meter
+   Keio University
+   5322 Endo, Fujisawa, Kanagawa
+   252-0882
+   Japan
+   Email: rdv@sfc.wide.ad.jp
+
+
+   Bruno Rijsman
+   Individual
+   Email: brunorijsman@gmail.com
+
+
+   Angela Sara Cacciapuoti
+   University of Naples Federico II
+   Department of Electrical Engineering and Information Technologies
+   Claudio 21
+   80125 Naples
+   Italy
+   Email: angelasara.cacciapuoti@unina.it
+
+
+   Marcello Caleffi
+   University of Naples Federico II
+   Department of Electrical Engineering and Information Technologies
+   Claudio 21
+   80125 Naples
+   Italy
+   Email: marcello.caleffi@unina.it
+
+
+   Shota Nagayama
+   Mercari, Inc.
+   Roppongi Hills Mori Tower 18F
+   6-10-1 Roppongi, Minato-ku, Tokyo
+   106-6118
+   Japan
+   Email: shota.nagayama@mercari.com