Recovering quantum information via classical channels

Quantum secret sharing is an important multipartite cryptographic protocol in which a quantum state\r\n(secret) is shared among a set of n players. The secret is distributed in such a way that it can only be\r\nrecovered by certain authorized subsets of players acting collaboratively. The recovery procedure assumes\r\nthat all players are interconnected through quantum channels, or, equivalently, that the players are allowed\r\nto perform non-local quantum operations. However, for practical applications, the consumption of quantum\r\ncommunication resources such as entanglement or quantum channels needs to minimized.\r\nWe provide a novel scheme in which quantum communication is replaced by local operations and classical\r\ncommunication (LOCC). Our protocol is based on embedding a classical maximum distance separable (MDS)\r\ncode into a quantum error correcting code and employing the properties of the latter. Our scheme is appealing\r\nfor real-world scenarios where the implementation of two-qubit gates is challenging. We illustrate the results\r\nby simple examples. Our methods constitute a rst step towards attacking the important problem of decoding\r\nquantum error correcting codes by LOCC.