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 qubit 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.

中文翻译：

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基于单个 Qudit 的可验证量子秘密共享

为了检测一些内部参与者或外部攻击者的欺诈行为，已经提出了一些可验证的阈值量子秘密共享方案。在本文中，我们使用双变量多项式基于单个量子位提出了一种新的可验证阈值结构。首先，Alice 选择一个非对称二元多项式，并将该多项式中的一对值发送给每个参与者。然后 Alice 和参与者在基于无偏基的 $d$ 维量子态上依次实现酉变换，其中这些酉变换与该多项式联系在一起。最后，安全性分析表明，与现有方案相比，所提出的方案可以检测来自外部和内部攻击的欺诈，并且与最近的方案具有可比性。