Internet-Draft | Quantum Internet Application Scenarios | March 2023 |

Wang, et al. | Expires 11 September 2023 | [Page] |

- Workgroup:
- QIRG
- Internet-Draft:
- draft-irtf-qirg-quantum-internet-use-cases-15
- Published:
- Intended Status:
- Informational
- Expires:

# Application Scenarios for the Quantum Internet

## Abstract

The Quantum Internet has the potential to improve application functionality by incorporating quantum information technology into the infrastructure of the overall Internet. This document provides an overview of some applications expected to be used on the Quantum Internet and categorizes them. Some general requirements for the Quantum Internet are also discussed. The intent of this document is to describe a framework for applications, and describe a few selected application scenarios for the Quantum Internet.¶

## Status of This Memo

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This Internet-Draft will expire on 11 September 2023.¶

## 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. Code Components extracted from this document must include Revised BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Revised BSD License.¶

## 1. Introduction

The Classical Internet has been constantly growing since it first became commercially popular in the early 1990's. It essentially consists of a large number of end nodes (e.g., laptops, smart phones, network servers) connected by routers and clustered in Autonomous Systems. The end nodes may run applications that provide service for the end users such as processing and transmission of voice, video or data. The connections between the various nodes in the Internet include backbone links (e.g., fiber optics) and access links (e.g., fiber optics, WiFi, cellular wireless, Digital Subscriber Lines (DSLs)). Bits are transmitted across the Classical Internet in packets.¶

Research and experiments have picked up over the last few years for developing the Quantum Internet [Wehner]. End nodes will also be part of the Quantum Internet, in that case called quantum end nodes that may be connected by quantum repeaters/routers. These quantum end nodes will also run value-added applications which will be discussed later.¶

The physical layer quantum channels between the various nodes in the Quantum Internet can be either waveguides such as optical fibers or free space. Photonic channels are particularly useful because light (photons) is very suitable for physically realizing qubits. The Quantum Internet will operate according to quantum physical principles such as quantum superposition and entanglement [I-D.irtf-qirg-principles].¶

The Quantum Internet is not anticipated to replace, but rather to enhance the Classical Internet and/or provide breakthrough applications. For instance, quantum key distribution can improve the security of the Classical Internet; quantum computing can expedite and optimize computation-intensive tasks in the Classical Internet. The Quantum Internet will run in conjunction with the Classical Internet. The process of integrating the Quantum Internet with the Classical Internet is similar to, but with more profound implications, the process of introducing any new communication and networking paradigm into the existing Internet. The intent of this document is to provide a common understanding and framework of applications and application scenarios for the Quantum Internet. It is noted that ITU-T SG13-TD158/WP3 [ITUT] briefly describes four kinds of use cases of quantum networks beyond quantum key distribution networks: quantum time synchronization use cases, quantum computing use cases, quantum random number generator use cases, and quantum communication use cases (e.g., quantum digital signatures, quantum anonymous transmission, and quantum money). This document focuses on quantum applications that have more impact on networking such as secure communication setup, secure quantum computing with privacy preservation, and distributed quantum computing; although these applications were mentioned in [ITUT], this document gives more details and derives some requirements from networking perspective.¶

This document represents the consensus of the Quantum Internet Research Group (QIRG). It has been reviewed extensively by Research Group (RG) members with expertise in both quantum physics and Classical Internet operation.¶

## 2. Terms and Acronyms List

This document assumes that the reader is familiar with the quantum information technology related terms and concepts that are described in [I-D.irtf-qirg-principles]. In addition, the following terms and acronyms are defined herein for clarity:¶

- Bell Pairs - A special type of two-qubits quantum state. The two qubits show a correlation that cannot be observed in classical information theory. We refer to such correlation as quantum entanglement. Bell pairs exhibit the maximal quantum entanglement. One example of a Bell pair is (|00>+|11>)/(Sqrt(2)). The Bell pairs are a fundamental resource for quantum communication.¶
- Bit - Binary Digit (i.e., fundamental unit of information in classical communications and classical computing).¶
- Classical Internet - The existing, deployed Internet (circa 2020) where bits are transmitted in packets between nodes to convey information. The Classical Internet supports applications which may be enhanced by the Quantum Internet. For example, the end-to-end security of a Classical Internet application may be improved by secure communication setup using a quantum application.¶
- Entanglement Swapping: It is a process of sharing an entanglement between two distant parties via some intermediate nodes. For example, suppose there are three parties A, B, C, and each of the parties (A, B) and (B, C) share Bell pairs. B can use the qubits it shares with A and C to perform entanglement swapping operations, and as a result, A and C share Bell pairs.¶
- Fast Byzantine Negotiation - A Quantum-based method for fast agreement in Byzantine negotiations [Ben-Or] [Taherkhani].¶
- Local Operations and Classical Communication (LOCC) - A method where nodes communicate in rounds, in which (1) they can send any classical information to each other; (2) they can perform local quantum operations individually; and (3) the actions performed in each round can depend on the results from previous rounds.¶
- Noisy Intermediate-Scale Quantum (NISQ) - NISQ was defined in [Preskill] to represent a near-term era in quantum technology. According to this definition, NISQ computers have two salient features: (1) The size of NISQ computers range from 50 to a few hundred physical qubits (i.e., intermediate-scale); and (2) Qubits in NISQ computers have inherent errors and the control over them is imperfect (i.e., noisy).¶
- Packet - A self-identified message with in-band addresses or other information that can be used for forwarding the message. The message contains an ordered set of bits of determinate number. The bits contained in a packet are classical bits.¶
- Prepare-and-Measure - A set of Quantum Internet scenarios where quantum nodes only support simple quantum functionalities (i.e., prepare qubits and measure qubits). For example, BB84 [BB84] is a prepare-and-measure quantum key distribution protocol.¶
- Quantum Computer (QC) - A quantum end node that also has quantum memory and quantum computing capabilities is regarded as a full-fledged quantum computer.¶
- Quantum End Node - An end node that hosts user applications and interfaces with the rest of the Internet. Typically, an end node may serve in a client, server, or peer-to-peer role as part of the application. A quantum end node must also be able to interface to the Classical Internet for control purposes and thus also be able to receive, process, and transmit classical bits/packets.¶
- Quantum Internet - A network of Quantum Networks. The Quantum Internet is expected to be merged into the Classical Internet. The Quantum Internet may either improve classical applications or may enable new quantum applications.¶
- Quantum Key Distribution (QKD) - A method that leverages quantum mechanics such as no-cloning theorem to let two parties create the same arbitrary classical key.¶
- Quantum Network - A new type of network enabled by quantum information technology where quantum resources such as qubits and entanglement are transferred and utilized between quantum nodes. The Quantum Network will use both quantum channels, and classical channels provided by the Classical Internet, referred to as a hybrid implementation.¶
- Quantum Teleportation - A technique for transferring quantum information via local operations and classical communication (LOCC). If two parties share a Bell pair, then using quantum teleportation a sender can transfer a quantum data bit to a receiver without sending it physically via a quantum channel.¶
- Qubit - Quantum Bit (i.e., fundamental unit of information in quantum communication and quantum computing). It is similar to a classic bit in that the state of a qubit is either "0" or "1" after it is measured, and is denoted as its basis state vector |0> or |1> using Dirac's ket notation. However, the qubit is different than a classic bit in that the qubit can be in a linear combination of both states before it is measured and termed to be in superposition. Any of several Degrees of Freedom (DOF) of a photon (e.g., polarization, time bib, and/or frequency) or an electron (e.g., spin) can be used to encode a qubit.¶
- Transmit a Qubit - An operation of encoding a qubit into a mobile carrier (i.e., typically photon) and passing it through a quantum channel from a sender (a transmitter) to a receiver.¶
- Teleport a Qubit - An operation on two or more carriers in succession to move a qubit from a sender to a receiver using quantum teleportation.¶
- Transfer a Qubit - An operation to move a qubit from a sender to a receiver without specifying the means of moving the qubit, which could be "transmit" or "teleport".¶

## 3. Quantum Internet Applications

### 3.1. Overview

The Quantum Internet is expected to be beneficial for a subset of existing and new applications. The expected applications for the Quantum Internet are still being developed as we are in the formative stages of the Quantum Internet [Castelvecchi] [Wehner]. However, an initial (and non-exhaustive) list of the applications to be supported on the Quantum Internet can be identified and classified using two different schemes. Note, this document does not include quantum computing applications that are purely local to a given node.¶

### 3.2. Classification by Application Usage

Applications may be grouped by the usage that they serve. Specifically, applications may be grouped according to the following categories:¶

- Quantum cryptography applications - Refer to the use of quantum information technology for cryptographic tasks (e.g., quantum key distribution [Renner]).¶
- Quantum sensors applications - Refer to the use of quantum information technology for supporting distributed sensors (e.g., clock synchronization [Jozsa2000] [Komar] [Guo] ).¶
- Quantum computing applications - Refer to the use of quantum information technology for supporting remote quantum computing facilities (e.g., distributed quantum computing [Denchev]).¶

This scheme can be easily understood by both a technical and non-technical audience. The next sections describe the scheme in more detail.¶

#### 3.2.1. Quantum Cryptography Applications

Examples of quantum cryptography applications include quantum-based secure communication setup and fast Byzantine negotiation.¶

- Secure communication setup - Refers to secure cryptographic key distribution between two or more end nodes. The most well-known method is referred to as Quantum Key Distribution (QKD) [Renner].¶
- Fast Byzantine negotiation - Refers to a Quantum-based method for fast agreement in Byzantine negotiations [Ben-Or], for example, to reduce the number of expected communication rounds and in turn achieve faster agreement, in contrast to classical Byzantine negotiations. A quantum aided Byzantine agreement on quantum repeater networks as proposed in [Taherkhani] includes optimization techniques to greatly reduce the quantum circuit depth and the number of qubits in each node. Quantum-based methods for fast agreement in Byzantine negotiations can be used for improving consensus protocols such as practical Byzantine Fault Tolerance(pBFT), as well as other distributed computing features which use Byzantine negotiations.¶
- Quantum money - The main security requirement of money is unforgeability. A quantum money scheme aims to fulfill by exploiting the no-cloning property of the unknown quantum states. Though the original idea of quantum money dates back to 1970, these early protocols allow only the issuing bank to verify a quantum banknote. However, the recent protocols such as public-key quantum money [Zhandry] allow anyone to verify the banknotes locally.¶

#### 3.2.2. Quantum Sensing/Metrology Applications

The entanglement, superposition, interference, squeezing properties can enhance the sensitivity of the quantum sensors and eventually can outperform the classical strategies. Examples of quantum sensor applications include network clock synchronization, high sensitivity sensing, etc. These applications mainly leverage a network of entangled quantum sensors (i.e. quantum sensor networks) for high-precision multi-parameter estimation [Proctor].¶

- Network clock synchronization - Refers to a world wide set of high-precision clocks connected by the Quantum Internet to achieve an ultra precise clock signal [Komar] with fundamental precision limits set by quantum theory.¶
- High sensitivity sensing - Refers to applications that leverage quantum phenomena to achieve reliable nanoscale sensing of physical magnitudes. For example, [Guo] uses an entangled quantum network for measuring the average phase shift among multiple distributed nodes.¶
- Interferometric Telescopes using Quantum Information - Interferometric techniques are used to combine signals from two or more telescopes to obtain measurements with higher resolution than what could be obtained with either telescope individually. It can make measurements of very small astronomical objects if the telescopes are spread out over a wide area. However, the phase fluctuations and photon loss introduced by the communication channel between the telescopes put a limitation on the baseline lengths of the optical interferometers. This limitation can be potentially avoided using quantum teleportation. In general, by sharing EPR-pairs using quantum repeaters, the optical interferometers can communicate photons over long distances, providing arbitrarily long baselines [Gottesman2012].¶

#### 3.2.3. Quantum Computing Applications

In this section, we include the applications for the quantum computing. It's anticipated that quantum computers as a cloud service will become more available in future. Sometimes, to run such applications in the cloud while preserving the privacy, a client and a server need to exchange qubits. Therefore, such privacy preserving quantum computing applications require a Quantum Internet to execute.¶

Examples of quantum computing include distributed quantum computing and secure quantum computing with privacy preservation, which can enable new types of cloud computing.¶

- Distributed quantum computing - Refers to a collection of remote small-capacity quantum computers (i.e., each supporting a relatively small number of qubits) that are connected and work together in a coordinated fashion so as to simulate a virtual large capacity quantum computer [Wehner].¶
- Secure quantum computing with privacy preservation - Refers to private, or blind, quantum computation, which provides a way for a client to delegate a computation task to one or more remote quantum computers without disclosing the source data to be computed over [Fitzsimons].¶

## 4. Selected Quantum Internet Application Scenarios

The Quantum Internet will support a variety of applications and deployment configurations. This section details a few key application scenarios which illustrates the benefits of the Quantum Internet. In system engineering, an application scenario is typically made up of a set of possible sequences of interactions between nodes and users in a particular environment and related to a particular goal. This will be the definition that we use in this section.¶

### 4.1. Secure Communication Setup

In this scenario, two banks (i.e., Bank #1 and Bank #2) need to have secure communications for transmitting important financial transaction records (see Figure 1). For this purpose, they first need to securely share a classic secret cryptographic key (i.e., a sequence of classical bits), which is triggered by an end-user banker at Bank #1. This results in a quantum node A at Bank #1 to securely establish a classical secret key with a quantum node B at Bank #2. This is referred to as a secure communication setup. Note that the quantum node A and B may be either a bare-bone quantum end node or a full-fledged quantum computer. This application scenario shows that the Quantum Internet can be leveraged to improve the security of Classical Internet applications of which the financial application shown in Figure 1 is an example.¶

One requirement for this secure communication setup process is that it should not be vulnerable to any classical or quantum computing attack. This can be realized using QKD which is unbreakable in principle. QKD can securely establish a secret key between two quantum nodes, using a classical authentication channel and insecure quantum channel without physically transmitting the key through the network and thus achieving the required security. However, care must be taken to ensure that the QKD system is safe against physical side channel attacks which can compromise the system. An example of a physical side channel attack is to surreptitiously inject additional light into the optical devices used in QKD to learn side information about the system such as the polarization. Other specialized physical attacks against QKD also use a classical authentication channel and insecure quantum channel such as the phase-remapping attack, photon number splitting attack, and decoy state attack [Zhao2018]. QKD can be used for many other cryptographic communications, such as IPSec and Transport Layer Security (TLS) where involved parties need to establish a shared security key, although it usually introduces a high latency.¶

QKD is the most mature feature of the quantum information technology, and has been commercially released in small-scale and short-distance deployments. More QKD use cases are described in ETSI documents [ETSI-QKD-UseCases]; in addition, the ETSI document [ETSI-QKD-Interfaces] specifies interfaces between QKD users and QKD devices.¶

In general, the prepare and measure QKD protocols (e.g., [BB84]) without using entanglement work as follows:¶

- The quantum node A encodes classical bits to qubits. Basically, the node A generates two random classical bit strings X, Y. Among them, it uses the bit string X to choose the basis and uses Y to choose the state corresponding to the chosen basis. For example, if X=0 then in case of BB84 protocol Alice prepares the state in {|0>, |1>}-basis; otherwise she prepares the state in {|+>, |->}-basis. Similarly, if Y=0 then Alice prepares the qubit either |0> or |+> (depending on the value of X), and if Y =1, then Alice prepares the qubit either |1> or |->.¶
- The quantum node A sends qubits to the quantum node B via quantum channel.¶
- The quantum node B receives qubits and measures each of them in one of the two basis at random.¶
- The quantum node B informs the quantum node A of its choice of basis for each qubit.¶
- The quantum node A informs the quantum node B which random quantum basis is correct.¶
- Both nodes discard any measurement bit under different quantum basis and remaining bits could be used as the secret key. Before generating the final secret key, there is a post-processing procedure over authenticated classical channels. The classical post-processing part can be subdivided into three steps, namely parameter estimation, error-correction, and privacy amplification. In the parameter estimation phase, both Alice and Bob use some of the bits to estimate the channel error. If it is larger than some threshold value, they abort the protocol otherwise move to the error-correction phase. Basically, if an eavesdropper tries to intercept and read qubits sent from node A to node B, the eavesdropper will be detected due to the entropic uncertainty relation property theorem of quantum mechanics. As a part of the post-processing procedure, both nodes usually also perform information reconciliation [Elkouss] for efficient error correction and/or conduct privacy amplification [Tang] for generating the final information-theoretical secure keys.¶
- The post-processing procedure needs to be performed over an authenticated classical channel. In other words, the quantum node A and the quantum node B need to authenticate the classical channel to make sure there is no eavesdroppers or man-in-the-middle attacks, according to certain authentication protocols such as [Kiktenko]. In [Kiktenko], the authenticity of the classical channel is checked at the very end of the post-processing procedure instead of doing it for each classical message exchanged between the quantum node A and the quantum node B.¶

It is worth noting that:¶

- There are many enhanced QKD protocols based on [BB84]. For example, a series of loopholes have been identified due to the imperfections of measurement devices; there are several solutions to take into account these attacks such as measurement-device-independent QKD [Zhang2019]. These enhanced QKD protocols can work differently than the steps of BB84 protocol [BB84].¶
- For large-scale QKD, QKD Networks (QKDN) are required, which can be regarded as a subset of a Quantum Internet. A QKDN may consist of a QKD application layer, a QKD network layer, and a QKD link layer [Qin]. One or multiple trusted QKD relays [Zhang2018] may exist between the quantum node A and the quantum node B, which are connected by a QKDN. Alternatively, a QKDN may rely on entanglement distribution and entanglement-based QKD protocols; as a result, quantum-repeaters/routers instead of trusted QKD relays are needed for large-scale QKD.¶
- QKD provides an information-theoretical way to share secret keys between two parties in the presence of Eve. However, this is true in theory, and there is a significant gap between theory and practice. By exploiting the imperfection of the detectors Eve can gain information about the shared key [Xu]. To avoid such side-channel attacks in [Lo], the researchers provide a QKD protocol called Measurement Device-Independent (MDI) QKD that allows two users (a transmitter "Alice" and a receiver "Bob") to communicate with perfect security, even if the (measurement) hardware they are using has been tampered with (e.g., by an eavesdropper) and thus is not trusted. It is achieved by measuring correlations between signals from Alice and Bob rather than the actual signals themselves.¶
- QKD protocols based on Continuous Variable (CV-QKD) have recently seen plenty of interest as they only require telecommunications equipment that is readily available and is also in common use industry-wide. This kind of technology is a potentially high-performance technique for secure key distribution over limited distances. The recent demonstration of CV-QKD shows compatibility with classical coherent detection schemes that are widely used for high bandwidth classical communication systems [Grosshans]. Note that we still do not have a quantum repeater for the continuous variable systems; hence, this kind of QKD technologies can be used for the short distance communications or trusted relay-based QKD networks.¶
- Secret sharing can be used to distribute a secret key among multiple nodes by letting each node know a share or a part of the secret key, while no single node can know the entire secret key. The secret key can only be re-constructed via collaboration from a sufficient number of nodes. Quantum Secret Sharing (QSS) typically refers to the scenario: The secret key to be shared is based on quantum states instead of classical bits. QSS enables to split and share such quantum states among multiple nodes.¶
- There are some entanglement-based QKD protocols, such as [Treiber][E91][BBM92], which work differently than the above steps. The entanglement-based schemes, where entangled states are prepared externally to the quantum node A and the quantum node B, are not normally considered "prepare-and-measure" as defined in [Wehner]; other entanglement-based schemes, where entanglement is generated within the source quantum node can still be considered "prepare-and-measure"; send-and-return schemes can still be "prepare-and-measure", if the information content, from which keys will be derived, is prepared within the quantum node A before being sent to the quantum node B for measurement.¶

As a result, the Quantum Internet in Figure 1 contains quantum channels. And in order to support secure communication setup especially in large-scale deployment, it also requires entanglement generation and entanglement distribution [I-D.van-meter-qirg-quantum-connection-setup], quantum repeaters/routers, and/or trusted QKD relays.¶

### 4.2. Secure Quantum Computing with Privacy Preservation

Secure computation with privacy preservation refers to the following scenario:¶

- A client node with source data delegates the computation of the source data to a remote computation node (i.e. a server).¶
- Furthermore, the client node does not want to disclose any source data to the remote computation node, which preserves the source data privacy.¶
- Note that there is no assumption or guarantee that the remote computation node is a trusted entity from the source data privacy perspective.¶

As an example illustrated in Figure 2, a terminal node can be a small quantum computer with limited computation capability compared to a remote quantum computation node (e.g., a remote mainframe quantum computer), but the terminal node needs to run a computation-intensive task (e.g., Shor’s factoring algorithm). The terminal node can create individual qubits and send them to the remote quantum computation node. Then, the remote quantum computation node can entangle the qubits, calculate on them, measure them, generate measurement results in classical bits, and return the measurement results to the terminal node. It is noted that those measurement results will look like purely random data to the remote quantum computation node because the initial states of the qubits were chosen in a cryptographically secure fashion.¶

As a new client/server computation model, BQC generally enables: 1) The client delegates a computation function to the server; 2) The client does not send original qubits to the server, but send transformed qubits to the server; 3) The computation function is performed at the server on the transformed qubits to generate temporary result qubits, which could be quantum-circuit-based computation or measurement-based quantum computation. The server sends the temporary result qubits to the client; 4) The client receives the temporary result qubits and transforms them to the final result qubits. During this process, the server can not figure out the original qubits from the transformed qubits. Also, it will not take too much efforts on the client side to transform the original qubits to the transformed qubits, or transform the temporary result qubits to the final result qubits. One of the very first BQC protocols such as [Childs] follows this process, although the client needs some basic quantum features such as quantum memory, qubit preparation and measurement, and qubit transmission. Measurement-based quantum computation is out of the scope of this document and more details about it can be found in [Jozsa2005].¶

It is worth noting that:¶

- The BQC protocol in [Childs] is a circuit-based BQC model, where the client only performs simple quantum circuit for qubit transformation, while the server performs a sequence of quantum logic gates. Qubits are transmitted back and forth between the client and the server.¶
- Universal BQC in [Broadbent] is a measurement-based BQC model, which is based on measurement-based quantum computing leveraging entangled states. The principle in UBQC is based on the fact the quantum teleportation plus a rotated Bell measurement realizes a quantum computation, which can be repeated multiple times to realize a sequence of quantum computation. In this approach, the client first prepares transformed qubits and sends them to the server and the server needs first to prepare entangled states from all received qubits. Then, multiple interaction and measurement rounds happen between the client and the server. For each round, the client computes and sends new measurement instructions or measurement adaptations to the server; then, the server performs the measurement according to the received measurement instructions to generate measurement results (qubits or in classic bits); the client receives the measurement results and transforms them to the final results.¶
- A hybrid universal BQC is proposed in [Zhang2009], where the server performs both quantum circuits like [Childs] and quantum measurements like [Broadbent] to reduce the number of required entangled states in [Broadbent]. Also, the client is much simpler than the client in [Childs]. This hybrid BQC is a combination of circuit-based BQC model and measurement-based BQC model.¶
- It will be ideal if the client in BQC is a purely classical client, which only needs to interact with the server using classical channel and communications. [Huang] demonstrates such an approach, where a classical client leverages two entangled servers to perform BQC, with the assumption that both servers cannot communicate with each other; otherwise, the blindness or privacy of the client cannot be guaranteed. The scenario as demonstrated in [Huang] is essentially an example of BQC with multiple servers.¶
- How to verify that the server will perform what the client requests or expects is an important issue in many BQC protocols, referred to as verifiable BQC. [Fitzsimons] discusses this issue and compares it in various BQC protocols.¶

In Figure 2, the Quantum Internet contains quantum channels and quantum repeaters/routers for long-distance qubits transmission [I-D.irtf-qirg-principles].¶

### 4.3. Distributed Quantum Computing

There can be two types of distributed quantum computing [Denchev]:¶

- Leverage quantum mechanics to enhance classical distributed computing. For example, entangled quantum states can be exploited to improve leader election in classical distributed computing, by simply measuring the entangled quantum states at each party (e.g., a node or a device) without introducing any classical communications among distributed parties [Pal]. Normally, pre-shared entanglement needs first be established among distributed parties, followed by LOCC operations at each party. And it generally does not need to transfer qubits among distributed parties.¶
- Distribute quantum computing functions to distributed quantum computers. A quantum computing task or function (e.g., quantum gates) is split and distributed to multiple physically separate quantum computers. And it may or may not need to transmit qubits (either inputs or outputs) among those distributed quantum computers. Entangled states will be needed and actually consumed to support such distributed quantum computing tasks. It is worth noting that: 1)Entangled states can be created beforehand and stored or buffered; 2) The rate of entanglement creation will limit the performance of practical quantum internet applicaitons including distributed quantum computing, although entangled states could be buffered. For example, [Gottesman1999] and [Eisert] have proved that a CNOT gate can be realized jointly by and distributed to multiple quantum computers. The rest of this section focuses on this type of distributed quantum computing.¶

As a scenario for the second type of distributed quantum computing, Noisy Intermediate-Scale Quantum (NISQ) computers distributed in different locations are available for sharing. According to the definition in [Preskill], a NISQ computer can only realize a small number of qubits and has limited quantum error correction. This scenario is referred to as distributed quantum computing [Caleffi] [Cacciapuoti2020] [Cacciapuoti2019]. This application scenario reflects the vastly increased computing power which quantum computers as a part of the Quantum Internet can bring, in contrast to classical computers in the Classical Internet, in the context of distributed quantum computing ecosystem [Cuomo]. According to [Cuomo], quantum teleportation enables a new communication paradigm, referred to as teledata [VanMeter2006-01], which moves quantum states among qubits to distributed quantum computers. In addition, distributed quantum computation also needs the capability of remotely performing quantum computation on qubits on distributed quantum computers, which can be enabled by the technique called telegate [VanMeter2006-02].¶

As an example, a user can leverage these connected NISQ computers to solve highly complex scientific computation problems, such as analysis of chemical interactions for medical drug development [Cao] (see Figure 3). In this case, qubits will be transmitted among connected quantum computers via quantum channels, while the user's execution requests are transmitted to these quantum computers via classical channels for coordination and control purpose. Another example of distributed quantum computing is secure Multi-Party Quantum Computation (MPQC) [Crepeau], which can be regarded as a quantum version of classical secure Multi-Party Computation (MPC). In a secure MPQC protocol, multiple participants jointly perform quantum computation on a set of input quantum states, which are prepared and provided by different participants. One of the primary aims of the secure MPQC is to guarantee that each participant will not know input quantum states provided by other participants. Secure MPQC relies on verifiable quantum secret sharing [Lipinska].¶

For the example shown in Figure 3, we want to move qubits from one NISQ computer to another NISQ computer. For this purpose, quantum teleportation can be leveraged to teleport sensitive data qubits from one quantum computer A to another quantum computer B. Note that Figure 3 does not cover measurement-based distributed quantum computing, where quantum teleportation may not be required. When quantum teleportation is employed, the following steps happen between A and B. In fact, LOCC [Chitambar] operations are conducted at the quantum computers A and B in order to achieve quantum teleportation as illustrated in Figure 3.¶

- The quantum computer A locally generates some sensitive data qubits to be teleported to the quantum computer B.¶
- A shared entanglement is established between the quantum computer A and the quantum computer B (i.e., there are two entangled qubits: q1 at A and q2 at B). For example, the quantum computer A can generate two entangled qubits (i.e., q1 and q2) and sends q2 to the quantum computer B via quantum communications.¶
- Then, the quantum computer A performs a Bell measurement of the entangled qubit q1 and the sensitive data qubit.¶
- The result from this Bell measurement will be encoded in two classical bits, which will be physically transmitted via a classical channel to the quantum computer B.¶
- Based on the received two classical bits, the quantum computer B modifies the state of the entangled qubit q2 in the way to generate a new qubit identical to the sensitive data qubit at the quantum computer A.¶

In Figure 3, the Quantum Internet contains quantum channels and quantum repeaters/routers [I-D.irtf-qirg-principles]. This application scenario needs to support entanglement generation and entanglement distribution (or quantum connection) setup [I-D.van-meter-qirg-quantum-connection-setup] in order to support quantum teleportation.¶

## 5. General Requirements

### 5.1. Background

Quantum technologies are steadily evolving and improving. Therefore, it is hard to predict the timeline and future milestones of quantum technologies as pointed out in [Grumbling] for quantum computing. Currently, a NISQ computer can achieve fifty to hundreds of qubits with some given error rate.¶

On the network level, six stages of Quantum Internet development are described in [Wehner] as follows:¶

- Trusted repeater networks (Stage-1)¶
- Prepare and measure networks (Stage-2)¶
- Entanglement distribution networks (Stage-3)¶
- Quantum memory networks (Stage-4)¶
- Fault-tolerant few qubit networks (Stage-5)¶
- Quantum computing networks (Stage-6)¶

The first stage is simple trusted repeater networks, while the final stage is the quantum computing networks where the full-blown Quantum Internet will be achieved. Each intermediate stage brings with it new functionality, new applications, and new characteristics. Figure 4 illustrates Quantum Internet application scenarios as described in this document mapped to the Quantum Internet stages described in [Wehner]. For example, secure communication setup can be supported in Stage-1, Stage-2, or Stage-3, but with different QKD solutions. More specifically:¶

In Stage-1, basic QKD is possible and can be leveraged to support secure communication setup but trusted nodes are required to provide end-to-end security. The primary requirement is the trusted nodes.¶

In Stage-2, the end users can prepare and measure the qubits. In this stage, the users can verify classical passwords without revealing it.¶

In Stage-3, end-to-end security can be enabled based on quantum repeaters and entanglement distribution, to support the same secure communication setup application. The primary requirement is entanglement distribution to enable long-distance QKD.¶

In Stage-4, the quantum repeaters gain the capability of storing and manipulating entangled qubits in the quantum memories. Using these kind of quantum networks, one can run sophisticated applications like blind quantum computing, leader election, quantum secret sharing.¶

In Stage-5, quantum repeaters can perform error correction; hence they can perform fault-tolerant quantum computations on the received data. With the help of these repeaters, it is possible to run distributed quantum computing and quantum sensor applications over a smaller number of qubits.¶

Finally, in Stage-6, distributed quantum computing relying on more qubits can be supported.¶

### 5.2. Requirements

Some general and functional requirements on the Quantum Internet from the networking perspective, based on the above application scenarios, are identified as follows:¶

- Methods for facilitating quantum applications to interact efficiently with entangled qubits are necessary in order for them to trigger distribution of designated entangled qubits to potentially any other quantum node residing in the Quantum Internet. To accomplish this, specific operations must be performed on entangled qubits (e.g., entanglement swapping, entanglement distillation). Quantum nodes may be quantum end nodes, quantum repeaters/routers, and/or quantum computers.¶
- Quantum repeaters/routers should support robust and efficient entanglement distribution in order to extend and establish high-fidelity entanglement connection between two quantum nodes. For achieving this, it is required to first generate an entangled pair on each hop of the path between these two nodes, and then perform entanglement swapping operations at each of the intermediate nodes.¶
- Quantum end nodes must send additional information on classical channels to aid in transferring qubits across quantum repeaters/receivers. This is because qubits are transferred individually and do not have any associated packet header which can help in transferring the qubit. Any extra information to aid in routing, identification, etc., of the qubit(s) must be sent via classical channels.¶
- Methods for managing and controlling the Quantum Internet including quantum nodes and their quantum resources are necessary. The resources of a quantum node may include quantum memory, quantum channels, qubits, established quantum connections, etc. Such management methods can be used to monitor network status of the Quantum Internet, diagnose and identify potential issues (e.g. quantum connections), and configure quantum nodes with new actions and/or policies (e.g. to perform a new entanglement swapping operation). New management information model for the Quantum Internet may need to be developed.¶

## 6. Conclusion

This document provides an overview of some expected application categories for the Quantum Internet, and then details selected application scenarios. The applications are first grouped by their usage which is a natural and easy to understand classification scheme. This set of applications may, of course, naturally expand over time as the Quantum Internet matures. Finally, some general requirements for the Quantum Internet are also provided.¶

This document can also serve as an introductory text to readers interested in learning about the practical uses of the Quantum Internet. Finally, it is hoped that this document will help guide further research and development of the Quantum Internet functionality required to implement the application scenarios described herein.¶

## 7. IANA Considerations

This document requests no IANA actions.¶

## 8. Security Considerations

This document does not define an architecture nor a specific protocol for the Quantum Internet. It focuses instead on detailing application scenarios, requirements, and describing typical Quantum Internet applications. However, some salient observations can be made regarding security of the Quantum Internet as follows.¶

It has been identified in [NISTIR8240] that once large-scale quantum computing becomes reality that it will be able to break many of the public-key (i.e., asymmetric) cryptosystems currently in use. This is because of the increase in computing ability with quantum computers for certain classes of problems (e.g., prime factorization, optimizations). This would negatively affect many of the security mechanisms currently in use on the Classical Internet which are based on public-key (Diffie-Hellman) encryption. This has given strong impetus for starting development of new cryptographic systems that are secure against quantum computing attacks [NISTIR8240].¶

Interestingly, development of the Quantum Internet will also mitigate the threats posed by quantum computing attacks against Diffie-Hellman based public-key cryptosystems. Specifically, the secure communication setup feature of the Quantum Internet as described in Section 4.1 will be strongly resistant to both classical and quantum computing attacks against Diffie-Hellman based public-key cryptosystems.¶

A key additional threat consideration for the Quantum Internet is pointed to by [RFC7258], which warns of the dangers of pervasive monitoring as a widespread attack on privacy. Pervasive monitoring is defined as a widespread, and usually covert, surveillance through intrusive gathering of application content or protocol metadata such as headers. This can be accomplished through active or passive wiretaps, traffic analysis, or subverting the cryptographic keys used to secure communications.¶

The secure communication setup feature of the Quantum Internet as described in Section 4.1 will be strongly resistant to pervasive monitoring based on directly attacking (Diffie-Hellman) encryption keys. Also, Section 4.2 describes a method to perform remote quantum computing while preserving the privacy of the source data. Finally, the intrinsic property of qubits to decohere if they are observed, albeit covertly, will theoretically allow detection of unwanted monitoring in some future solutions.¶

Modern networks are implemented with zero trust principles where classical cryptography is used for confidentiality, integrity protection, and authentication on many of the logical layers of the network stack, often all the way from device to software in the cloud [NISTSP800-207]. The cryptographic solutions in use today are based on well-understood primitives, provably secure protocols and state-of-the-art implementations that are secure against a variety of side-channel attacks.¶

In contrast to conventional cryptography and Post-Quantum Cryptography (PQC), the security of QKD is inherently tied to the physical layer, which makes the threat surfaces of QKD and conventional cryptography quite different. QKD implementations have already been subjected to publicized attacks [Zhao2008] and the National Security Agency (NSA) notes that the risk profile of conventional cryptography is better understood [NSA]. The fact that conventional cryptography and PQC are implemented at a higher layer than the physical one means PQC can be used to securely send protected information through untrusted relays. This is in stark contrast with QKD, which relies on hop-by-hop security between intermediate trusted nodes. The PQC approach is better aligned with the modern technology environment, in which more applications are moving toward end-to-end security and zero-trust principles. It is also important to note that while PQC can be deployed as a software update, QKD requires new hardware.¶

Regarding QKD implementation details, the NSA states that communication needs and security requirements physically conflict in QKD and that the engineering required to balance them has extremely low tolerance for error. While conventional cryptography can be implemented in hardware in some cases for performance or other reasons, QKD is inherently tied to hardware. The NSA points out that this makes QKD less flexible with regard to upgrades or security patches. As QKD is fundamentally a point-to-point protocol, the NSA also notes that QKD networks often require the use of trusted relays, which increases the security risk from insider threats.¶

The UK’s National Cyber Security Centre cautions against reliance on QKD, especially in critical national infrastructure sectors, and suggests that PQC as standardized by the NIST is a better solution [NCSC]. Meanwhile, the National Cybersecurity Agency of France has decided that QKD could be considered as a defense-in-depth measure complementing conventional cryptography, as long as the cost incurred does not adversely affect the mitigation of current threats to IT systems [ANNSI].¶

## 9. Acknowledgments

The authors want to thank Michele Amoretti, Mathias Van Den Bossche, Xavier de Foy, Patrick Gelard, Álvaro Gómez Iñesta, Wojciech Kozlowski, John Mattsson, Rodney Van Meter, Joey Salazar, and Joseph Touch, and the rest of the QIRG community as a whole for their very useful reviews and comments to the document.¶

## 10. Informative References

- [ANNSI]
- "Should Quantum Key Distribution be Used for Secure Communications?", Technical Position Paper, French National Cybersecurity Agency (ANSSI), , <https://www.ssi.gouv.fr/en/publication/should-quantum-key-distribution-be-used-for-secure-communications/>.
- [BB84]
- Bennett, C. H. and G. Brassard, "Quantum Cryptography: Public Key Distribution and Coin Tossing", , <http://researcher.watson.ibm.com/researcher/files/us-bennetc/BB84highest.pdf>.
- [BBM92]
- Bennett, C.H., Brassard, G., and N.D. Mermin, "Quantum Cryptography without Bell's Theorem", Physical Review Letter, American Physical Society, , <https://link.aps.org/doi/10.1103/PhysRevLett.68.557>.
- [Ben-Or]
- Ben-Or, M. and A. Hassidim, "Fast Quantum Byzantine Agreement", SOTC, ACM, , <https://dl.acm.org/doi/10.1145/1060590.1060662>.
- [Broadbent]
- Broadbent, A. and et. al., "Universal Blind Quantum Computation", 50th Annual Symposium on Foundations of Computer Science, IEEE, , <https://arxiv.org/pdf/0807.4154.pdf>.
- [Cacciapuoti2019]
- Cacciapuoti, A.S. and et. al., "When Entanglement meets Classical Communications: Quantum Teleportation for the Quantum Internet", , <https://arxiv.org/abs/1907.06197>.
- [Cacciapuoti2020]
- Cacciapuoti, A.S. and et. al., "Quantum Internet: Networking Challenges in Distributed Quantum Computing", IEEE Network, January 2020, , <https://ieeexplore.ieee.org/document/8910635>.
- [Caleffi]
- Caleffi, M. and et. al., "Quantum internet: From Communication to Distributed Computing!", NANOCOM, ACM, , <https://dl.acm.org/doi/10.1145/3233188.3233224>.
- [Cao]
- Cao, Y. and et. al., "Potential of Quantum Computing for Drug Discovery", Journal of Research and Development, IBM, , <https://doi.org/10.1147/JRD.2018.2888987>.
- [Castelvecchi]
- Castelvecchi, D., "The Quantum Internet has arrived (and it hasn't)", Nature 554, 289-292, , <https://www.nature.com/articles/d41586-018-01835-3>.
- [Childs]
- Childs, A. M., "Secure Assisted Quantum Computation", , <https://arxiv.org/pdf/quant-ph/0111046.pdf>.
- [Chitambar]
- Chitambar, E. and et. al., "Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)", Communications in Mathematical Physics, Springer, , <https://link.springer.com/article/10.1007/s00220-014-1953-9>.
- [Crepeau]
- Crepeau, C. and et. al., "Secure Multi-party Quantum Computation", 34th Symposium on Theory of Computing (STOC), ACM, , <https://doi.org/10.1145/509907.510000>.
- [Cuomo]
- Cuomo, D. and et. al., "Towards a Distributed Quantum Computing Ecosystem", Quantum Communication, IET, , <http://dx.doi.org/10.1049/iet-qtc.2020.0002>.
- [Denchev]
- Denchev, V.S. and et. al., "Distributed Quantum Computing: A New Frontier in Distributed Systems or Science Fiction?", SIGACT News ACM, , <https://doi.org/10.1145/1412700.1412718>.
- [E91]
- Ekert, A.K., "Quantum Cryptography with Bell's Theorem", Physical Review Letter, American Physical Society, , <https://link.aps.org/doi/10.1103/PhysRevLett.67.661>.
- [Eisert]
- Eisert, J. and et. al., "Optimal Local Implementation of Nonlocal Quantum Gates", Physical Review A, American Physical Society, , <https://doi.org/10.1103/PhysRevA.101.032332>.
- [Elkouss]
- Elkouss, D. and et. al., "Information Reconciliation for Quantum Key Distribution", , <https://arxiv.org/pdf/1007.1616.pdf>.
- [ETSI-QKD-Interfaces]
- ETSI GR QKD 003 V2.1.1, "Quantum Key Distribution (QKD); Components and Internal Interfaces", , <https://www.etsi.org/deliver/etsi_gr/QKD/001_099/003/02.01.01_60/gr_QKD003v020101p.pdf>.
- [ETSI-QKD-UseCases]
- ETSI GR QKD 002 V1.1.1, "Quantum Key Distribution (QKD); Use Cases", , <https://www.etsi.org/deliver/etsi_gs/qkd/001_099/002/01.01.01_60/gs_qkd002v010101p.pdf>.
- [Fitzsimons]
- Fitzsimons, J. F., "Private Quantum Computation: An Introduction to Blind Quantum Computing and Related Protocols", , <https://www.nature.com/articles/s41534-017-0025-3.pdf>.
- [Gottesman1999]
- Gottesman, D. and I. Chuang, "Demonstrating the Viability of Universal Quantum Computation using Teleportation and Single-Qubit Operations", Nature 402, 390-393, , <https://doi.org/10.1038/46503>.
- [Gottesman2012]
- Gottesman, D., Jennewein, T., and S. Croke, "Longer-Baseline Telescopes Using Quantum Repeaters", Physical Review Letter, American Physical Society, , <https://link.aps.org/doi/10.1103/PhysRevLett.109.070503>.
- [Grosshans]
- Grosshans, F. and P. Grangier, "Continuous Variable Quantum Cryptography Using Coherent States", Physical Review Letters, American Physical Society, , <https://doi.org/10.1103/PhysRevLett.88.057902>.
- [Grumbling]
- Grumbling, E. and M. Horowitz, "Quantum Computing: Progress and Prospects", National Academies of Sciences, Engineering, and Medicine, The National Academies Press, , <https://doi.org/10.17226/25196>.
- [Guo]
- Guo, X. and et. al., "Distributed Quantum Sensing in a Continuous-Variable Entangled Network", Nature Physics, Nature, , <https://www.nature.com/articles/s41567-019-0743-x>.
- [Hill]
- Hill, R.M. and et. al., "A Tool for Functional Brain Imaging with Lifespan Compliance", Nature Communications 10, 4785(2019), , <https://doi.org/10.1038/s41467-019-12486-x>.
- [Huang]
- Huang, H. and et. al., "Experimental Blind Quantum Computing for a Classical Client", , <https://arxiv.org/pdf/1707.00400.pdf>.
- [I-D.dahlberg-ll-quantum]
- Dahlberg, A., Skrzypczyk, M., and S. Wehner, "The Link Layer service in a Quantum Internet", Work in Progress, Internet-Draft, draft-dahlberg-ll-quantum-03, , <https://datatracker.ietf.org/doc/html/draft-dahlberg-ll-quantum-03>.
- [I-D.irtf-qirg-principles]
- Kozlowski, W., Wehner, S., Van Meter, R., Rijsman, B., Cacciapuoti, A. S., Caleffi, M., and S. Nagayama, "Architectural Principles for a Quantum Internet", Work in Progress, Internet-Draft, draft-irtf-qirg-principles-11, , <https://datatracker.ietf.org/doc/html/draft-irtf-qirg-principles-11>.
- [I-D.van-meter-qirg-quantum-connection-setup]
- Van Meter, R. and T. Matsuo, "Connection Setup in a Quantum Network", Work in Progress, Internet-Draft, draft-van-meter-qirg-quantum-connection-setup-01, , <https://datatracker.ietf.org/doc/html/draft-van-meter-qirg-quantum-connection-setup-01>.
- [ITUT]
- ITU-T SG13-TD158/WP3, "Draft New Technical Report ITU-T TR.QN-UC:"Use Cases of Quantum Networks beyond QKDN"", , <https://www.itu.int/md/T22-SG13-221125-TD-WP3-0158/en>.
- [Jozsa2000]
- Josza, R., Abrams, D.S., Dowling, J.P., and C.P. Williams, "Quantum Clock Synchronization Based on Shared Prior Entanglement", Physical Review Letter, American Physical Society, , <https://link.aps.org/doi/10.1103/PhysRevLett.85.2010>.
- [Jozsa2005]
- Josza, R. and et. al., "An Introduction to Measurement based Quantum Computation", , <https://arxiv.org/pdf/quant-ph/0508124.pdf>.
- [Kiktenko]
- Kiktenko, E.O. and et. al., "Lightweight Authentication for Quantum Key Distribution", , <https://arxiv.org/pdf/1903.10237.pdf>.
- [Komar]
- Komar, P. and et. al., "A Quantum Network of Clocks", , <https://arxiv.org/pdf/1310.6045.pdf>.
- [Lipinska]
- Lipinska, V. and et. al., "Verifiable Hybrid Secret Sharing with Few Qubits", Physical Review A, American Physical Society, , <https://doi.org/10.1103/PhysRevA.101.032332>.
- [Lo]
- Lo, H.-K. and et. al., "Experimental Demonstration of Phase-Remapping Attack in a Practical Quantum Key Distribution System", Physical Review Letters, American Physical Society, , <https://doi.org/10.1103/PhysRevLett.108.130503>.
- [NCSC]
- "Quantum Security Technologies", White Paper, National Cyber Security Centre (NCSC), , <https://www.ncsc.gov.uk/whitepaper/quantum-security-technologies>.
- [NISTIR8240]
- Alagic, G. and et. al., "Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process", NISTIR 8240, , <https://nvlpubs.nist.gov/nistpubs/ir/2019/NIST.IR.8240.pdf>.
- [NISTSP800-207]
- Rose, S. J., Borchert, O., Mitchell, S., and S. Connelly, "NIST, Zero Trust Architecture", Special Publication (NIST SP) - 800-207, National Institute of Standards and Technology (NIST), , <https://doi.org/10.6028/NIST.SP.800-207>.
- [NSA]
- National Security Agency, "Post-Quantum Cybersecurity Resources", <https://www.nsa.gov/Cybersecurity/Post-Quantum-Cybersecurity-Resources/>.
- [Pal]
- Pal, S.P. and et. al., "Multi-partite Quantum Entanglement versus Randomization: Fair and Unbiased Leader Election in Networks", , <https://arxiv.org/pdf/quant-ph/0306195.pdf>.
- [Preskill]
- Preskill, J., "Quantum Computing in the NISQ Era and Beyond", , <https://arxiv.org/pdf/1801.00862>.
- [Proctor]
- Proctor, T.J. and et. al., "Multiparameter Estimation in Networked Quantum Sensors", Physical Review Letters, American Physical Society, , <https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.080501>.
- [Qin]
- Qin, H., "Towards Large-Scale Quantum Key Distribution Network and Its Applications", , <https://www.itu.int/en/ITU-T/Workshops-and-Seminars/2019060507/Documents/Hao_Qin_Presentation.pdf>.
- [Renner]
- Renner, R., "Security of Quantum Key Distribution", , <https://arxiv.org/pdf/quant-ph/0512258.pdf>.
- [RFC2119]
- Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/info/rfc2119>.
- [RFC7258]
- Farrell, S. and H. Tschofenig, "Pervasive Monitoring Is an Attack", BCP 188, RFC 7258, DOI 10.17487/RFC7258, , <https://www.rfc-editor.org/info/rfc7258>.
- [Taherkhani]
- Taherkhani, M.A., Navi, K., and R. Van Meter, "Resource-Aware System Architecture Model for Implementation of Quantum Aided Byzantine Agreement on Quantum Repeater Networks", Quantum Science and Technology, IOP, , <https://dl.acm.org/doi/10.1145/1060590.1060662>.
- [Tang]
- Tang, B. and et. al., "High-speed and Large-scale Privacy Amplification Scheme for Quantum Key Distribution", Scientific Reports, Nature Research, , <https://doi.org/10.1038/s41598-019-50290-1>.
- [Treiber]
- Treiber, A. and et. al., "A Fully Automated Entanglement-based Quantum Cyptography System for Telecom Fiber Networks", New Journal of Physics, 11, 045013, , <https://doi.org/10.1364/OE.26.024260>.
- [VanMeter2006-01]
- Van Meter, R. and et. al., "Distributed Arithmetic on a Quantum Multicomputer", 33rd International Symposium on Computer Architecture (ISCA) IEEE, , <https://doi.org/10.1109/ISCA.2006.19>.
- [VanMeter2006-02]
- Van Meter, R. and et. al., "Architecture of a Quantum Multicompuer Optimized for Shor's Factoring Algorithm", , <https://arxiv.org/pdf/quant-ph/0607065.pdf>.
- [Wang]
- Wang, C. and et. al., "Quantum Secure Direct Communication with High-Dimension Quantum Superdense Coding", Physical Review A, American Physical Society, , <https://doi.org/10.1103/PhysRevA.71.044305>.
- [Wehner]
- Wehner, S., Elkouss, D., and R. Hanson, "Quantum internet: A vision for the road ahead", Science 362, , <http://science.sciencemag.org/content/362/6412/eaam9288.full>.
- [Xu]
- Xu, F. and et. al., "Experimental Demonstration of Phase-Remapping Attack in a Practical Quantum Key Distribution System", New Journal of Physics, 12 113026, , <https://iopscience.iop.org/article/10.1088/1367-2630/12/11/113026>.
- [Zhandry]
- Zhandry, M., "Quantum Lightning Never Strikes the Same State Twice", 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Darmstadt, Germany, May 19-23, 2019, Proceedings, Part III, , <http://doi.org/10.1007/978-3-030-17659-4_14>.
- [Zhang2009]
- Zhang, X. and et. al., "A Hybrid Universal Blind Quantum Computation", Information Sciences, Elsevier, , <https://www.sciencedirect.com/science/article/abs/pii/S002002551930458X>.
- [Zhang2018]
- Zhang, Q., Hu, F., Chen, Y., Peng, C., and J. Pan, "Large Scale Quantum Key Distribution: Challenges and Solutions", Optical Express, OSA, , <https://doi.org/10.1364/OE.26.024260>.
- [Zhang2019]
- Zhang, P. and et. al., "Integrated Relay Server for Measurement-Device-Independent Quantum Key Distribution", , <https://arxiv.org/abs/1912.09642>.
- [Zhao2008]
- Zhao, Y., Fung, C.-H., Qi, B., Chen, C., and H.K. Lo, "Experimental Demonstration of Time-Shift Attack against Practical Quantum Key Distribution Systems", Physical Review A, American Physical Society, , <https://link.aps.org/doi/10.1103/PhysRevA.78.042333>.
- [Zhao2018]
- Zhao, Y., "Development of Quantum Key Distribution and Attacks against it", Journal of Physics, J. Phys, , <https://iopscience.iop.org/article/10.1088/1742-6596/1087/4/042028>.