Genuine secret-sharing states

Quantum secret sharing allows each player to have classical information for secret sharing in quantum mechanical ways. In this work, we construct a class of quantum states on which players can quantumly perform secret-sharing secure against dishonest players as well as eavesdropper. We here call them the genuine secret-sharing states. In addition, we show that if N players share an N-party genuine secret-sharing state, then arbitrary M players out of the total players can share an M-party genuine secret-sharing state by means of local operations and classical communication on the state, where N>M >= 2. We also define the distillable rate with respect to the genuine secret-sharing state and explain the connection between the distillable rate and the relative entropy of entanglement.

Automated summary

Quantum secret sharing is achieved through constructing specific quantum states in this work, allowing participants to securely share information. The article also demonstrates a method for N players to share an N-party genuine secret-sharing state, and explains the connection between the distillable rate and the relative entropy of entanglement.