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Advanced Quantum Technologies

Flexible Quantum Network Coding by Using Quantum Multiplexing

Yu‐Guang Yang, Bing‐Xin Liu, Guang‐Bao Xu, Dong‐Huan Jiang, Yi‐Hua Zhou, Wei‐Min Shi, Tao Shang

Published Jun 4, 2024• 9 citations
Publisher

Abstract

Abstract Quantum 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.

DOI
10.1002/qute.202400016

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Classical network coding uses encoding of information over networks to achieve secure and high throughput communication with low latency. Its quantum analog, namely Quantum Network Coding (QNC) is a promising protocol to achieve quantum communication over quantum networks. In this paper, we propose a method for establishing QNC in Measurement-Based Quantum Computing (MBQC), which is a universal quantum computational model. We demonstrate that the problem of multiple unicast or multiple multicast of distinct computational basis states over a quantum network can be solved by simulating existing classical networks, with the CNOT implementation in MBQC as a basis for transmitting and encoding of states. We also show how it can be further extended to simultaneously distribute the Bell pairs and Greenberger–Horne–Zeilinger (GHZ) states required for quantum communication between distant transmitter and corresponding receiver nodes of a network.
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.
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.
As a specific example of network coding, the butterfly network often represents the networks with bottlenecks. In this paper, we propose a typical butterfly quantum network coding scheme based on remote state preparation of arbitrary two-qubit states with the assistance of GHZ channels. Firstly, in a butterfly network, each source node simultaneously performs two appropriate projective measurements under suitable measurement basis on their own qubits. Next, their measurement results would be distributed to mid-side nodes. In the following, midside nodes perform encoded operations and send their encoded information to destination nodes. Finally, two destination nodes obtain the target state according to all information they receive with the success probability 1.
Motivated by multi-step quantum teleportation of single-qubit states and two-qubit states with entanglement swapping, we present a small scale quantum network communication scheme based on entanglement of Bell states. In this scheme, it contains certain number of single-qubit quantum source nodes that teleport unknown quantum states to other nodes in the network in the multi-teleport fashion where every intermediate node can pass on any of its received quantum information to others via multi-step quantum teleportation. It makes legal nodes more convenient than any other previous schemes to transmit unknown quantum states to unknown participants in practical applications. The security of this scheme is based on the securely-shared quantum channels between all nodes.
Abstract Future quantum internet applications will derive their power from the ability to share quantum information across the network1,2. Quantum teleportation allows for the reliable transfer of quantum information between distant nodes, even in the presence of highly lossy network connections3. Although many experimental demonstrations have been performed on different quantum network platforms4–10, moving beyond directly connected nodes has, so far, been hindered by the demanding requirements on the pre-shared remote entanglement, joint qubit readout and coherence times. Here we realize quantum teleportation between remote, non-neighbouring nodes in a quantum network. The network uses three optically connected nodes based on solid-state spin qubits. The teleporter is prepared by establishing remote entanglement on the two links, followed by entanglement swapping on the middle node and storage in a memory qubit. We demonstrate that, once successful preparation of the teleporter is heralded, arbitrary qubit states can be teleported with fidelity above the classical bound, even with unit efficiency. These results are enabled by key innovations in the qubit readout procedure, active memory qubit protection during entanglement generation and tailored heralding that reduces remote entanglement infidelities. Our work demonstrates a prime building block for future quantum networks and opens the door to exploring teleportation-based multi-node protocols and applications2,11–13.