论文标题
通过完整的正交基础，构建一般对称性构成阳性阳性 - 阳性 - 操作员值措施
Construction of general symmetric-informationally-complete-positive-operator-valued measures by using a complete orthogonal basis
论文作者
论文摘要
已知一般的对称性内部完整（GSIC） - 阳性 - 启动器值测量（POVM）在最小的IC POVM中提供具有固定平均纯度的最佳量子状态层析成像。在本文中，我们通过完整的正交基础（COB）提供了GSIC POVM的一般结构，该结构也被解释为正常的准生产性表示。证明COB的光谱特性在SIC POVM的构建中起着关键作用，也是对状态断层扫描的均方误差的界限。特别是，为任何D构建SIC POVM的必要条件是由COB的痕迹的功率建设性地给出的。我们给出了三个简单的蛋糕结构，从中可以系统地从中获得GSIC POVM。
A general symmetric-informationally-complete (GSIC)-positive-operator-valued measure (POVM) is known to provide an optimal quantum state tomography among minimal IC POVMs with a fixed average purity. In this paper we provide a general construction of a GSIC POVM by means of a complete orthogonal basis (COB), also interpreted as a normal quasiprobability representation. A spectral property of a COB is shown to play a key role in the construction of SIC POVMs and also for the bound of the mean-square error of the state tomography. In particular, a necessary and sufficient condition to construct a SIC POVM for any d is constructively given by the power of traces of a COB. We give three simple constructions of COBs from which one can systematically obtain GSIC POVMs.
