SCIENCE CHINA Information Sciences, Volume 62, Issue 1: 012501(2019) https://doi.org/10.1007/s11432-018-9592-9

Efficient quantum state transmission via perfect quantum network coding

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  • ReceivedMar 4, 2018
  • AcceptedAug 7, 2018
  • PublishedNov 22, 2018


Quantum network coding with the assistance of auxiliary resources can achieve perfect transmission of the quantum state. This paper suggests a novel perfect network coding scheme to efficiently solve the quantum $k$-pair problem, in which only a few assisting resources are introduced. Specifically, only one pair of maximally entangled state needs to be pre-shared between two intermediate nodes, and only $O(k)$ of classical information is transmitted though the network. Moreover, the classical communication used in our protocol does not cause transmission congestion, providing better adaptability to large-scale quantum $k$-pair networks.Through relevant analyses and comparisons, we demonstrate that our proposed scheme saves resources and has good application value, thereby showing its high efficiency. Furthermore, the proposed scheme achieves 1-max flow quantum communication, and the achievable rate region result is extended from its counterpart over the butterfly network.


This work was supported by National Natural Science Foundation of China (Grant Nos. 61671087, 61272514, 61170272, 61003287, 61373131), the Fok Ying Tong Education Foundation (Grant No. 131067), and the Major Science and Technology Support Program of Guizhou Province (Grant No. 20183001).


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  • Figure 1

    Classical network coding (CNC) over the butterfly network.

  • Figure 2

    Quantum $k$-pair network $\mathcal{N}$ as an extension of the butterfly network. Each source node $s_{i}$ is connected to $n_{1}$ and all receivers except $t_{i}$; each sink node $t_{i}$ is connected to $n_{2}$ and all senders except $s_{i}$.

  • Table 1   Comparison results of different quantum network coding schemes (QNCSs) under butterfly network
    2*QNCSs Prior entanglementClassical communication
    Location Pair number Total amount (bits)
    Hayashi [29] Source nodes 2 10
    Ma et al. [30] Source nodes 2 13
    Satoh et al. [31,32] Neighbor nodes 7 10
    Zhang et al. [33] Side nodes 2 10
    Wang et al. [36] Intermediate nodes 1 8
    Ours Intermediate nodes 1 6
  • Table 2   Comparison results of different quantum network coding schemes (QNCSs) under the $k$-pair network $\mathcal{N}$
    2*QNCSs Prior entanglementClassical communication
    Location Pair number Total amount (bits)
    Kobayashi et al. [41] $kM|V|\lceil\log~d\rceil$
    Kobayashi et al. [42] $2|E|\lceil\log~d\rceil$
    Mahdian et al. [34] Source nodes $k$ $2(k^2+k-1)\lceil\log~d\rceil$
    Li et al. [43] $(k^2+k-1)\lceil\log~d\rceil$
    Wang et al. [36] Intermediate nodes 1 $(3k+2)\lceil\log~d\rceil$
    Ours Intermediate nodes 1 $2(k+1)\lceil\log~d\rceil$

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