Minimum-error discrimination between self-symmetric mixed quantum state signals
Minimum-error discrimination between self-symmetric mixed quantum state signals
复制标题
自对称混合量子态信号之间的最小误差辨别
DOI：
10.1109/tit.2011.2170954
复制
发表时间：
2012
影响因子：
2.5
通讯作者：
K. Nakahira and T. S. Usuda
中科院分区：
文献类型：
--
作者：
井上優也;廣田悠介;木下和彦;戸出英樹;上孝三;渡辺尚;K. Nakahira and T. S. Usuda
我们推导出混合量子态信号的最小误差测量的一些性质，其中密度算子本身具有一定的对称性。在第一种情况下，我们表明，如果存在一个与混合状态信号的每个密度算子可交换的常规法线算子，则存在由检测算子组成的最佳测量，该检测算子表示为在常规法线算子的特征空间中具有支持的正算子的直接和。在第二种情况下，我们表明，对于阿贝尔几何均匀状态信号，如果表示某个基中的信号之一的矩阵具有所有实数元素，则表示该基中最佳测量的相应检测算子的矩阵也具有所有实数元素。此外，我们还讨论了这些属性的一些应用示例，并得出特殊情况下最佳测量的解析解。
We derive some properties of minimum-error measurements for mixed quantum state signals where a density operator itself has a certain symmetry. In the first case, we show that if there exists a regular normal operator that commutes with each density operator of mixed state signals, then there exists an optimal measurement that consists of detection operators expressed as the direct sum of positive operators with supports in the eigenspaces of the regular normal operator. In the second case, we show that for abelian geometrically uniform state signals, if a matrix which represents one of the signals in a certain basis has all real elements, then the matrix which represents the corresponding detection operator of an optimal measurement in that basis also has all real elements. In addition, we discuss some examples of applications of these properties and derive analytical solutions of optimal measurements for special cases.