Quantum Network Coding Research Articles

Flexible Quantum Network Coding by Using Quantum Multiplexing

AbstractQuantum network coding (QNC) aims at alleviating quantum communication congestion in quantum networks. Although several QNC protocols have been presented, they cannot meet the practical requirements that part of source nodes intend to transmit their quantum states with same or different qubit numbers via the bottleneck network simultaneously. Here, the study presents a flexible QNC protocol by using quantum multiplexing. First, the entangled pairs are generated between adjacent nodes in a heralded way by using quantum multiplexing. Then the quantum memories of the source nodes and the ones of the corresponding target nodes are entangled when the intermediate nodes execute multiple rounds of entanglement swapping operations on their quantum memories. Finally, the quantum states are transmitted from the source nodes to their corresponding target nodes by means of quantum teleportation. Compared with the existing protocols, the protocol allows an arbitrary part of the source nodes to transmit their quantum states with same or different qubit numbers via the bottleneck network simultaneously, thereby exhibiting its flexibility.

Heralded quantum network coding of multi-particle states based on quantum time-bin multiplexing

Quantum network coding can effectively alleviate bottlenecks in quantum networks thus improving the transmission efficiency and the throughput of the quantum network. Although various quantum network coding protocols have been constructed, most of them focus mainly on addressing the communication congestion issue of simultaneously transmitting single-qubit states via the bottleneck channel in quantum networks. In this paper, a protocol for the quantum two-pair unicast transmission of multi-particle states using quantum time-bin multiplexing is proposed. Parallel entanglement is established in a heralded way between two-dimensional quantum memories (QMs) of intermediate nodes by transmitting a high-dimensional encoded single photon via the bottleneck channel. Then the quantum unicast transmission of multi-particle states can be achieved by using quantum teleportation and the resultant entangled pairs. Additionally, a security enhanced protocol is presented when dishonest intermediate nodes or outside eavesdroppers are taken into account. No alternative measurements are needed to check security. This makes the present protocol cost-effective and efficient. Compared with existing methods, no pre-shared entangled states are required. This provides a new perspective for the development of quantum networks.

Symbolic model checking quantum circuits in Maude.

This article presents a symbolic approach to model checking quantum circuits using a set of laws from quantum mechanics and basic matrix operations with Dirac notation. We use Maude, a high-level specification/programming language based on rewriting logic, to implement our symbolic approach. As case studies, we use the approach to formally specify several quantum communication protocols in the early work of quantum communication and formally verify their correctness: Superdense Coding, Quantum Teleportation, Quantum Secret Sharing, Entanglement Swapping, Quantum Gate Teleportation, Two Mirror-image Teleportation, and Quantum Network Coding. We demonstrate that our approach/implementation can be a first step toward a general framework to formally specify and verify quantum circuits in Maude. The proposed way to formally specify a quantum circuit makes it possible to describe the quantum circuit in Maude such that the formal specification can be regarded as a series of quantum gate/measurement applications. Once a quantum circuit has been formally specified in the proposed way together with an initial state and a desired property expressed in linear temporal logic (LTL), the proposed model checking technique utilizes a built-in Maude LTL model checker to automatically conduct formal verification that the quantum circuit enjoys the property starting from the initial state.

High-dimensional multi-input quantum random access codes and mutually unbiased bases

Quantum random access codes (QRACs) provide a basic tool for demonstrating the advantages of quantum resources and protocols, which have a wide range of applications in quantum information processing tasks. However, the investigation and application of high-dimensional $(d)$ multi-input $(n)$ $n^{(d)}\rightarrow1$ QRACs are still lacking. Here, we present a general method to find the maximum success probability of $n^{(d)}\rightarrow1$ QRACs. In particular, we give the analytical solution for maximum success probability of $3^{(d)}\rightarrow1$ QRACs when measurement bases are mutually unbiased bases (MUBs). Based on the analytical solution, we show the relationship between MUBs and $n^{(d)}\rightarrow1$ QRACs. First, we provide a systematic method of searching for the operational inequivalence of MUBs (OI-MUBs) when the dimension $d$ is a prime power. Second, we theoretically prove that, surprisingly, the commonly used Galois MUBs are not the optimal measurement bases to obtain the maximum success probability of $n^{(d)}\rightarrow1$ QRACs, which indicates a breakthrough according to the traditional conjecture regarding the optimal measurement bases. Furthermore, based on high-fidelity high-dimensional quantum states of orbital angular momentum, we experimentally achieve two-input and three-input QRACs up to dimension 11. We experimentally confirm the OI-MUBs when $d=5$. Our results open alternative avenues for investigating the foundational properties of quantum mechanics and quantum network coding.

Quantum network coding via time-bin multiplexing

<p indent="0mm">Quantum network coding is used to overcome the congestion problem in quantum networks, which can effectively improve the transmission efficiency and total throughput of quantum networks. Here, we propose a time-bin complexing network coding method for crossly transmitting two arbitrary single-qubit states over the butterfly network. To solve the congestion problem, a single photon with polarization and time-bin degrees of freedom acts as a bridge to entangle the two-dimensional quantum memories of two intermediate nodes in a heralded way. Finally, quantum 2-pair unicast communication is completed based on quantum teleportation and the heralded double entangled channels. Concerning dishonest intermediate nodes being concerned, a security-enhanced quantum 2-pair unicast communication protocol is presented. Security and performance are analyzed, and the result shows that the improved protocol is secure against the general entangle-measure attack of intermediate nodes. It can be extended to multiple unicast communication over a more general quantum network by exploiting the time-bin complexing technique.

Asymmetric Quantum Multicast Network Coding: Asymmetric Optimal Cloning over Quantum Networks

Multicasting of quantum states is an essential feature of quantum internet. Since the noncloning theorem prohibits perfect cloning of an unknown quantum state, an appropriate protocol may depend on the purpose of the multicast. In this paper, we treat the multicasting of a single copy of an unknown state over a quantum network with free classical communication. We especially focus on protocols exactly multicasting an asymmetric optimal universal clone. Hence, these protocols are optimal and universal in terms of mean fidelity between input and output states, but the fidelities can depend on target nodes. Among these protocols, a protocol spending smaller communication resources is preferable. Here, we construct such a protocol attaining the min-cut of the network described as follows. Two (three) asymmetric optimal clones of an input state are created at a source node. Then, the state is divided into classical information and a compressed quantum state. The state is sent to two (three) target nodes using the quantum network coding. Finally, the asymmetric clones are reconstructed using LOCC with a small amount of entanglement shared among the target nodes and the classical information sent from the source node.

Quantum network coding based on six-qubit entangled state

In order to improve the security and transmission efficiency of quantum network coding (QNC), we propose a new QNC scheme based on butterfly network. The scheme uses two groups of GHZ states to distribute quantum entangled states through intermediate nodes, so as to establish the connection between multiple nodes and achieve safe and reliable quantum traffic. This paper can not only improve the security of QNC, but also reduce the transmission of particles and improve the anti-interference ability of information. Compared with the traditional network coding method based on a priori entanglement, our scheme is a better attempt.

A secure crossing two qubits protocol based on quantum homomorphic encryption

In order to solve the information leakage caused by dishonest intermediate nodes in quantum network coding, we apply quantum homomorphic encryption to the butterfly network, and propose a secure protocol for crossing two qubits. Firstly, in the communication process between two senders and the first intermediate node, two senders encrypt their measured particles and send them to the first intermediate node for encoding. If two intermediate nodes are dishonest and know the encryption rules between two senders and two receivers, or there is an external eavesdropper, none of them can recover the transmitted qubits of two senders from the encrypted transmitted particles. In this way, our protocol can transmit two qubits safely and crossly in the butterfly network. Secondly, by analyzing the internal participant attack and the external eavesdropper attack launched by dishonest intermediate nodes and an external eavesdropper respectively, it is confirmed that our protocol is secure. Finally, the experimental simulation results based on the Qiskit framework prove that our protocol is feasible.

Quantum Remote State Preparation Based on Quantum Network Coding

As an innovative theory and technology, quantum network coding has become the research hotspot in quantum network communications. In this paper, a quantum remote state preparation scheme based on quantum network coding is proposed. Comparing with the general quantum remote state preparation schemes, our proposed scheme brings an arbitrary unknown quantum state finally prepared remotely through the quantum network, by designing the appropriate encoding and decoding steps for quantum network coding. What is worth mentioning, from the network model, this scheme is built on the quantum k-pair network which is the expansion of the typical bottleneck network—butterfly network. Accordingly, it can be treated as an efficient quantum network preparation scheme due to the characteristics of network coding, and it also makes the proposed scheme more applicable to the large-scale quantum networks. In addition, the fact of an arbitrary unknown quantum state remotely prepared means that the senders do not need to know the desired quantum state. Thus, the security of the proposed scheme is higher. Moreover, this scheme can always achieve the success probability of 1 and 1-max flow of value k. Thus, the communication efficiency of the proposed scheme is higher. Therefore, the proposed scheme turns out to be practicable, secure and efficient, which helps to effectively enrich the theory of quantum remote state preparation.

Controllable Quantum Network Coding Scheme Based on Quantum Walk

Controllable Quantum Network Coding Scheme Based on Quantum Walk

A Practical Quantum Network Coding Protocol Based on Non-Maximally Entangled State

In many earlier works, perfect quantum state transmission over the butterfly network can be achieved via quantum network coding protocols with the assist of maximally entangled states. However, in actual quantum networks, a maximally entangled state as auxiliary resource is hard to be obtained or easily turned into a non-maximally entangled state subject to all kinds of environmental noises. Therefore, we propose a more practical quantum network coding scheme with the assist of non-maximally entangled states. In this paper, a practical quantum network coding protocol over grail network is proposed, in which the non-maximally entangled resource is assisted and even the desired quantum state can be perfectly transmitted. The achievable rate region, security and practicability of the proposed protocol are discussed and analyzed. This practical quantum network coding protocol proposed over the grail network can be regarded as a useful attempt to help move the theory of quantum network coding towards practicability.

Measurement-based Quantum Repeater Network Coding

Quantum network coding can effectively improve the aggregate throughput of quantum networks and alleviate bottlenecks caused by topological constraints. Most of previous schemes are dedicated to the efficient teleportation of unknown quantum states in a quantum network. Herein a proposal for transmission of deterministic known states over quantum repeater network based on quantum measurements. We show that the new protocol offers advantages over three aspects. Firstly, the senders in our protocol obtain the knowledge of the quantum state to be transmitted, which enables the autonomy of quantum network transmission. Secondly, we study the quantum repeater network coding for long-distance deterministic quantum state communication. Quantum repeater network initialization requires entanglement distribution only among neighboring nodes, greatly saving entanglement resources, channel overhead and storage costs. Thirdly, based on Pauli measurements and local complementation, new protocol realizes parallel coding operations to mitigate latency issues sufficiently. Combining quantum network coding and quantum remote state preparation technology, our protocol provides an important solution for deterministic known states transmission over large-scale quantum network in the future.

Controlled Quantum Network Coding Without Loss of Information

Controlled Quantum Network Coding Without Loss of Information

Continuous-Variable Quantum Network Coding Based on Quantum Discord

Continuous-Variable Quantum Network Coding Based on Quantum Discord

Anti-Noise Quantum Network Coding Protocol Based on Bell States and Butterfly Network Model

How to establish a secure and efficient quantum network coding algorithm is one of important research topics of quantum secure communications. Based on the butterfly network model and the characteristics of easy preparation o... | Find, read and cite all the research you need on Tech Science Press

Secure quantum network coding based on quantum homomorphic message authentication

As the principal security threat, pollution attacks also seriously affect the security of quantum network coding, just like they do for the classical network coding. Based on this, we first propose two secure quantum homomorphic message authentication schemes based on quantum circuit, which well resist the pollution attacks launched by outside attackers and the attackers including inside untrusted nodes over the general quantum network. Then, we apply this authentication method into our extended quantum network coding scheme over the multi-unicast network $$\mathcal {N}$$, solving the quantum k-pair problem securely and perfectly. Analysis results show that our proposed quantum network coding scheme has higher security and higher quantum communication rate, compared with the existing secure scheme.

Analysis of measurement-based quantum network coding over repeater networks under noisy conditions

Quantum network coding is an effective solution for alleviating bottlenecks in quantum networks. We introduce a measurement-based quantum network coding scheme for quantum repeater networks (MQNC), and analyze its behavior based on results acquired from Monte-Carlo simulation that includes various error sources over a butterfly network. By exploiting measurement-based quantum computing, operation on qubits for completing network coding proceeds in parallel. We show that such an approach offers advantages over other schemes in terms of the quantum circuit depth, and therefore improves the communication fidelity without disturbing the aggregate throughput. The circuit depth of our protocol has been reduced by 56.5% compared to the quantum network coding scheme (QNC) introduced in 2012 by Satoh, et al. For MQNC, we have found that the resulting entangled pairs' joint fidelity drops below 50% when the accuracy of local operations is lower than 98.9%, assuming that all initial Bell pairs across quantum repeaters have a fixed fidelity of 98%. Overall, MQNC showed substantially higher error tolerance compared to QNC and slightly better than buffer space multiplexing using step-by-step entanglement swapping, but not quite as strong as simultaneous entanglement swapping operations.

The solvability of quantum k-pair network in a measurement-based way

Network coding is an effective means to enhance the communication efficiency. The characterization of network solvability is one of the most important topic in this field. However, for general network, the solvability conditions are still a challenge. In this paper, we consider the solvability of general quantum k-pair network in measurement-based framework. For the first time, a detailed account of measurement-based quantum network coding(MB-QNC) is specified systematically. Differing from existing coding schemes, single qubit measurements on a pre-shared graph state are the only allowed coding operations. Since no control operations are concluded, it makes MB-QNC schemes more feasible. Further, the sufficient conditions formulating by eigenvalue equations and stabilizer matrix are presented, which build an unambiguous relation among the solvability and the general network. And this result can also analyze the feasibility of sharing k EPR pairs task in large-scale networks. Finally, in the presence of noise, we analyze the advantage of MB-QNC in contrast to gate-based way. By an instance network {G}_{k}, we show that MB-QNC allows higher error thresholds. Specially, for X error, the error threshold is about 30% higher than 10% in gate-based way. In addition, the specific expressions of fidelity subject to some constraint conditions are given.

Single-shot secure quantum network coding on butterfly network with free public communication

Quantum network coding on the butterfly network has been studied as a typical example of quantum multiple cast network. We propose a secure quantum network code for the butterfly network with free public classical communication in the multiple unicast setting under restricted eavesdropper’s power. This protocol certainly transmits quantum states when there is no attack. We also show the secrecy with shared randomness as additional resource when the eavesdropper wiretaps one of the channels in the butterfly network and also derives the information sending through public classical communication. Our protocol does not require verification process, which ensures single-shot security.

Continuous-variable quantum network coding for coherent states

As far as the spectral characteristic of quantum information is concerned, the existing quantum network coding schemes can be looked on as the discrete-variable quantum network coding schemes. Considering the practical advantage of continuous variables, in this paper, we explore two feasible continuous-variable quantum network coding (CVQNC) schemes. Basic operations and CVQNC schemes are both provided. The first scheme is based on Gaussian cloning and ADD/SUB operators and can transmit two coherent states across with a fidelity of 1/2, while the second scheme utilizes continuous-variable quantum teleportation and can transmit two coherent states perfectly. By encoding classical information on quantum states, quantum network coding schemes can be utilized to transmit classical information. Scheme analysis shows that compared with the discrete-variable paradigms, the proposed CVQNC schemes provide better network throughput from the viewpoint of classical information transmission. By modulating the amplitude and phase quadratures of coherent states with classical characters, the first scheme and the second scheme can transmit $$4{\log _2}N$$4log2N and $$2{\log _2}N$$2log2N bits of information by a single network use, respectively.