Genuine Secret-Sharing States

TL;DR

This paper introduces a new class of quantum states called genuine secret-sharing states, enabling secure quantum secret sharing among multiple players and demonstrating how smaller groups can share secret states via local operations and classical communication.

Contribution

The work constructs genuine secret-sharing states that are secure against dishonest players and eavesdroppers, and establishes their properties and relationships with entanglement measures.

Findings

Genuine secret-sharing states enable secure multi-party quantum secret sharing.

Any subset of players can share a smaller genuine secret-sharing state via local operations.

The distillable rate of these states relates to the relative entropy of entanglement.

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.