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arXiv:1801.03306 · IEEE Transactions on Information Theory

Secure Quantum Network Code Without Classical Communication

Seunghoan Song, Masahito Hayashi

Published Aug 6, 2019• 24 citations
arXivHTMLPDF

Abstract

We consider the secure quantum communication over a network with the presence of a malicious adversary who can eavesdrop and contaminate the states. The network consists of noiseless quantum channels with the unit capacity and the nodes which applies noiseless quantum operations. As the main result, when the maximum number m1of the attacked channels over the entire network uses is less than a half of the network transmission rate m0(i.e., m10/2), our code implements secret and correctable quantum communication of the rate m0- 2m1by using the network asymptotic number of times. Our code is universal in the sense that the code is constructed without the knowledge of the specific node operations and the network topology, but instead, every node operation is constrained to the application of an invertible matrix to the basis states. Moreover, our code requires no classical communication. Our code can be thought of as a generalization of the quantum secret sharing.

DOI
10.1109/tit.2019.2933422

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We consider the secure quantum communication over a network with the presence of a malicious adversary who can eavesdrop and contaminate the states. The network consists of noiseless quantum channels with the unit capacity and the nodes which applies noiseless quantum operations. As the main result, when the maximum number m1of the attacked channels over the entire network uses is less than a half of the network transmission rate m0(i.e., m10/2), our code implements secret and correctable quantum communication of the rate m0- 2m1by using the network asymptotic number of times. Our code is universal in the sense that the code is constructed without the knowledge of the specific node operations and the network topology, but instead, every node operation is constrained to the application of an invertible matrix to the basis states. Moreover, our code requires no classical communication. Our code can be thought of as a generalization of the quantum secret sharing.
We consider the secure quantum communication over a network with the presence of the malicious adversary who can eavesdrop and contaminate the states. The network consists of the noiseless quantum channels with unit capacity and the nodes which applies noiseless quantum operations. As the main result, when the maximum number m1of the attacked channels over the entire network uses is less than a half of network transmission rate m0(i.e., m10/2), our protocol implements secret and correctable quantum communication of rate m0- 2m1by using the network asymptotic number of times. Our protocol requires no classical communication and no knowledge of network structure, but instead, a node operation is limited to the application of an invertible matrix to the basis states. Our protocol can be thought of as a generalization of honest-dealer verifiable quantum secret sharing. A full version of this paper is accessible at: https://arxiv.org/pdf/1801.03306.pdf.
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 protocols for generating shared secret keys represent an effective method of ensuring secure information transmission using quantum communication channels. However, they are limited in scalability due to the physical constraints of quantum channels, which necessitates the use of classical communication channels for exchanging information between participants. This leads to the necessity of developing security threat models and network protection, especially in the case of hybrid networks, where quantum channels are used alongside classical ones. The peculiarity of constructing quantum key distribution protocols is associated with the costliness of implementation and implies the inevitable use of classical communication channels for key distribution. This paper addresses the task of ensuring the security of communication between subscribers not directly connected by quantum channels, through intermediary nodes, and analyzes threats from internal and external adversaries. Special attention is paid to situations where both types of adversaries have information about the processes and protocols in the network. The paper examines widely used key distribution protocols employed in practice. It describes the main security requirements applied to key distribution protocols, and presents the results of an analysis of the compliance of the discussed protocols with these requirements
This paper considers the communication over a quantum multiple-unicast network where r sender-receiver pairs communicate independent quantum states. We concretely construct a quantum network code for the quantum multiple-unicast network as a generalization of the code [Song and Hayashi, arxiv:1801.03306, 2018] for the quantum unicast network. When the given node operations are restricted to invertible linear operations between bit basis states and the rates of transmissions and interferences are restricted, our code certainly transmits a quantum state for each sender-receiver pair by n-use of the network asymptotically, which guarantees no information leakage to the other users. Our code is implemented only by the coding operation in the senders and receivers and employs no classical communication and no manipulation of the node operations. Several networks that our code can be applied are also given.
When there exists a malicious attacker in the network, we need to be careful of eavesdropping and contamination. This problem is crucial for network communication when the network is realized by a partially trusted relay of quantum key distribution. We discuss the asymptotic rate in a linear network with the secrecy and robustness conditions when the above type of attacker exists. Also, under the same setting, we discuss the asymptotic rate in a linear network when we impose the secrecy condition alone. Then, we apply these results to the network composed of a partially trusted relay of quantum key distribution, which enables us to realize secure long-distance communication via short-distance quantum key distribution.
This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general — indeed, it is impossible even for the simple butterfly network. As additional resource we allow free classical communication between any pair of network nodes. It is shown that perfect quantum network coding is achievable in this model whenever classical network coding is possible over the same network when replacing all quantum capacities by classical capacities. More precisely, it is proved that perfect quantum network coding using free classical communication is possible over a network with k source-target pairs if there exists a classical linear (or even vector-linear) coding scheme over a finite ring. Our proof is constructive in that we give explicit quantum coding operations for each network node. This paper also gives an upper bound on the number of classical communication required in terms of k, the maximal fan-in of any network node, and the size of the network. x1 x2 s1 ♠ s2 ♠ ❍❍❍❍ ❥ x1 x2 ✟ n1 x1 x1 ⊕ x2 x2 n2 ♠ x1 ⊕ x2✟ ❍❍❍❍ ❥ x1 ⊕ x2