Constructions of approximately mutually unbiased bases and sym-metric informationally complete positive operator-valued mea-sures by Gauss and Jacobi sums
Constructions of approximately mutually unbiased bases and sym-metric informationally complete positive operator-valued mea-sures by Gauss and Jacobi sums
复制标题
DOI：
10.1360/012012-186
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Weiyang Wang;Aixian Zhang;K. Feng
中科院分区：
文献类型：
--
作者：
Weiyang Wang;Aixian Zhang;K. Feng
相互无偏基的基础（MUB）和对称信息完全完整的正面运算符值措施（SIC-POVM）都是量子信息理论中的重要对象。尽管人们不知道是否存在一个完全的MUB来实现非PRIMEMER-POWER维度，但几个版本宽松的内部产品条件已经考虑了大约MUB的含量。因此，只有有限数量的k，因此在MUB情况下，已经找到了c K中的sicpovms。在本文中，我们使用了Klappenecker等人给出的近似MUB和SIC-POVM的定义，我们使用了Q Qlappenecker et al.for Prime Q，我们提供了Q的简单构造，我们介绍了Q的简单构造（AMUB）对于维Q-1，Q+1的Q+1 AMUB，用于尺寸Q-1，它显示了C K中AMUB的正顺序碱基的数量，可以大于K+1，而Q Gauss和Jacobi Sums的AMUB Q+1 Q+1。我们还介绍了Gauss Sum在dimension Q-1中的大约SIC-POVM（ASIC-POVM）的结构。
Mutually unbiased bases (MUB) and symmetric informationally complete positive operator-valued measure (SIC-POVM) are both important objects in quantum information theory.While people do not know if there exists a complete MUB for non-prime-power dimension,several versions of approximately MUB have been considered by relaxed the inner product condition.So far there are only finite number of K such that SICPOVMs in C k have been found.As in the MUB case,several versions of approximately SIC-POVM have been considered by relaxed the inner product condition.In this paper,we use the definitions of approximate MUB and SIC-POVM given by Klappenecker et al.For prime power q,we present simple constructions of q approximately MUB (AMUB) for dimension q-1,q+1 AMUB for dimension q-1,which shows the number of orthonormal bases of an AMUB in C k can be more than K+1,and q AMUB for dimension q+1 by Gauss and Jacobi sums.We also present a construction of approximately SIC-POVM (ASIC-POVM) in dimension q-1 by Gauss sum.