Efficient quantum state transmission via perfect quantum network coding

Abstract

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.