Tavakoli等利用奇素数维量子系统上互相无偏基以及基上酉变换的循环性质, 设计了一个基于互相无偏基上的d维单量子系统的秘密共享方案。 我们首先构造了偶数维量子系统上的一类标准正交基,并 给出相应结论,然后利用这类标准正交基和基上酉变换的性质提出了一个(N,N)门限量子秘密共享方案。 该方案与奇素数维系统上 的量子秘密共享方案相比,在测量方面的有效性提高为原来的2倍。 作为特例,给出了d=8时对应的基,酉阵及对应方案,最后就该方案相关的攻击进行了安全性讨论。

Tavakoli et al. used the cyclic property of the mutually unbiased basis and unitary transformations on it for the odd prime dimension, and designed a secret sharing scheme for d dimensional single quantum systems based on the mutually unbiased basis. Firstly, the class of standard orthogonal basis on even dimensional quantum systems is constructed, and relevant conclusions are given, and then an (N,N) threshold quantum secret sharing scheme based on the properties of the basis and unitary transformations on it is proposed. In contrast to Tavakoli’s scheme, the measurement efficiency of the proposed scheme has been doubled. And here are the corresponding basis, unitary matrix and related results about d=8 for illustration. Finally, the security of scheme related attacks is discussed.