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arXiv:1705.01474 · Quantum Science and Technology

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

Masaki Owari, Go Kato, Masahito Hayashi

Published Sep 6, 2017• 24 citations
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Abstract

Abstract 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.

DOI
10.1088/2058-9565/aa8ac4

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Abstract 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.
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.
Quantum network coding with classical assistance can transmit quantum information with fidelity one in error-free quantum channels. However, the dependency on classical network solutions leads to higher communication complexity and transmission congestion over a large-scale network with bottleneck channels. We find that certain types of quantum operation are sufficient to support multiple unicast sessions over the extended butterfly network. Furthermore, this construction decouples classical communication (assisting decoding information) from classical network solution. Based on this design, we propose an optimal protocol for this specific network, which significantly reduces the communication cost.
Based on the typical example of butterfly network,this paper promoted a quantum network coding scheme including the transmission of classical information and the unknown qubit.It improved effectively the overall performance of the network which could achieve the maximizing information transmission in quantum network.Remarkably,here it did not require classic channel,only had quantum channel.It mad use of qubit as register to transmit classical information.No matter what send was unknown qubit or classical bit,both could be encoded with register and decoded without classical assistant information.It's effective to improve security of this scheme.
With the development of quantum network, quantum continuous-variables have practical significance of improving communication. This paper proposes a new continuous-variable quantum network coding protocol (CVQNC) based on the butterfly network model with the hybrid channel of quantum channel and classical channel to realise the cross transmission of quantum information and classical information. The new protocol not only is conducive to the realisation of quantum network, but also can reduce the communication cost of quantum network effectively. It can be seen from the throughput and fidelity analysis that this protocol has a higher throughput than discrete-variable quantum network encoding scheme and classical information network encoding scheme. The ceiling of fidelity in this protocol is 4/9. According to the analysis of simple intercept attack and spectroscope attack, it is secure for the protocol to transmit quantum information and classical information by resisting on the eavesdropping attack of the third-party effectively.
With the development of quantum network, quantum continuous-variables have practical significance of improving communication. This paper proposes a new continuous-variable quantum network coding protocol (CVQNC) based on the butterfly network model with the hybrid channel of quantum channel and classical channel to realise the cross transmission of quantum information and classical information. The new protocol not only is conducive to the realisation of quantum network, but also can reduce the communication cost of quantum network effectively. It can be seen from the throughput and fidelity analysis that this protocol has a higher throughput than discrete-variable quantum network encoding scheme and classical information network encoding scheme. The ceiling of fidelity in this protocol is 4/9. According to the analysis of simple intercept attack and spectroscope attack, it is secure for the protocol to transmit quantum information and classical information by resisting on the eavesdropping attack of the third-party effectively.
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.