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Science China Information Sciences

Efficient quantum state transmission via perfect quantum network coding

Zhenzhen Li, Gang Xu, Xiu‐Bo Chen, Zhiguo Qu, Xinxin Niu, Yixian Yang

Published Nov 22, 2018• 21 citations
Publisher
DOI
10.1007/s11432-018-9592-9

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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
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.