Genuine Secret-Sharing States

Abstract

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. 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.

arXiv comment8 pages

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• Quantum cryptographic resource distillation and entanglement
• Investigating controlled teleportation capability of quantum states with respect to $k$-separability
• Scalable multiparty steering based on a single pair of entangled qubits