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Zhongguo kexue. Wulixue Lixue Tianwenxue

Quantum network coding via time-bin multiplexing

Feng Liu, Yu‐Guang Yang

Published Jun 22, 2022• 1 citation
Publisher

Abstract

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.

DOI
10.1360/sspma-2022-0172

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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.
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.
It is natural in a quantum network system that multiple users intend to send their quantum message to their respective receivers, which is called a multiple unicast quantum network. We propose a canonical method to derive a secure quantum network code over a multiple unicast quantum network from a secure classical network code. Our code correctly transmits quantum states when there is no attack. It also guarantees the secrecy of the transmitted quantum state even with the existence of an attack when the attack satisfies a certain natural condition. In our security proof, the eavesdropper is allowed to modify wiretapped information dependently on the previously wiretapped messages. Our protocol guarantees the secrecy by utilizing one-way classical information transmission (public communication) in the same direction as the quantum network although the verification of quantum information transmission requires two-way classical communication. In the protocol, some nodes may share secret randomness as resources in advance. Our secure network code can be applied to several networks including the butterfly network.
Inspired by the structure of the network coding over the butterfly network, a framework of quantum network coding scheme is investigated, which transmits two unknown quantum states crossly over the butterfly quantum system with the multi-photon non-maximally entangled GHZ states. In this scheme, it contains certain number of entanglement-qubit source nodes that teleport unknown quantum states to other nodes on the small-scale network where each intermediate node can pass on its received quantum states to others via superdense coding. In order to transmit the unknown states in a deterministic way, the controlled quantum teleportation is adopted on the intermediate node. It makes legal nodes more convenient than any other previous teleportation schemes to transmit unknown quantum states to unknown participants in applications. It shows that the intrinsic efficiency of transmissions approaches 100% in principle. This scheme is secure based on the securely-shared quantum channels between all nodes and the quantum mechanical impossibility of local unitary transformations between non-maximally entangled GHZ states. Moreover, the generalized scheme is proposed for transmitting two multipartite entangled states. DOI:  http://dx.doi.org/10.11591/telkomnika.v11i2.2031
Quantum networks require parallel quantum entanglement between pairs of distant quantum memories (QMs) for practical applications. However, usually one pair of QMs is entangled using a single photonic pulse and multiple pulses are consumed to generate parallel entanglement between pairs of QMs. We propose a multiplexing method for simultaneously entangling multiple pairs of QMs located in two distant nodes. A single photon with high-dimensional encoding first entangles with all QMs in one node, leading to hybrid entanglement between a high-dimensional photon and two-dimensional QMs, and then it interacts with QMs in the other node and converts the hybrid entanglement to entanglement between multiple pairs of QMs in a heralded way. This can significantly increase the efficiency of large-scale quantum networks by reducing the exponential transmission loss via time-bin multiplexing. Furthermore, this protocol presents a specific connection between high-dimensional and two-dimensional quantum systems.
This letter proposes new quantum network coding schemes based on controlled teleportation to control the decoding process of receivers in a butterfly network. Firstly, a quantum network coding scheme with two controllers is proposed based on the paradigm XQQ (crossing two qubits) protocol. Then the other scheme based on the perfect quantum network coding protocol with prior entanglement is designed for high fidelity. By introducing the controller, our schemes realize that the decoding process of unicast stream can be controlled, which is helpful to extend these schemes to a general network with unicast or multicast. Our schemes also provide a convenient model to combine authentication into quantum network and would be significant to enhance the security of quantum communication.
Abstract 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.