Verifiable Quantum Secret Sharing Based on a Single Qudit

To detect frauds from some internal participants or external attackers, some verifiable threshold quantum secret sharing schemes have been proposed. In this paper, we present a new verifiable threshold structure based on a single qudit using bivariate polynomial. First, Alice chooses an asymmetric bivariate polynomial and sends a pair of values from this polynomial to each participant. Then Alice and participants implement in sequence unitary transformation on the d-dimensional quantum state based on unbiased bases, where those unitary transformations are contacted by this polynomial. Finally, security analysis shows that the proposed scheme can detect the fraud from external and internal attacks compared with the exiting schemes and is comparable to the recent schemes.