论文标题
具有最佳单面区分性的两分量子测量
Bipartite quantum measurements with optimal single-sided distinguishability
论文作者
论文摘要
我们在复合$ n \ times n $ hilbert空间中分析了正交基础，该空间描述了两部分量子系统，并寻求具有最佳单侧相互区分性的基础。这种条件意味着在每个子系统中，$ n^2 $还原状态形成最大边缘长度的常规单纯形，该单纯性针对痕量距离定义。在情况下，两倍系统的$ n = 2 $，我们的解决方案与Gisin引入的优雅关节测量相吻合。我们以$ n = 3 $的形式得出一个类似星座的明确表达，并提供了$ n^2 $状态的一般结构，在$ {\ cal H} _n \ otimes {\ cal H} _n $中形成了最佳基础。我们的构建对于已知对称信息（SIC）广义测量的所有维度都是有效的。此外，我们表明，区分复合系统最佳基础状态的一党测量会导致具有线性重建公式的局部量子状态层析成像。最后，我们使用两台不同的IBM计算机对一个单个量子组的三个相互无偏基底座进行了整个三个相互偏见的基础，测试了引入的层析成分方案。
We analyse orthogonal bases in a composite $N\times N$ Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the $N^2$ reduced states form a regular simplex of a maximal edge length, defined with respect to the trace distance. In the case $N=2$ of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We derive explicit expressions of an analogous constellation for $N=3$ and provide a general construction of $N^2$ states forming such an optimal basis in ${\cal H}_N \otimes {\cal H}_N$. Our construction is valid for all dimensions for which a symmetric informationally complete (SIC) generalized measurement is known. Furthermore, we show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography with a linear reconstruction formula. Finally, we test the introduced tomographical scheme on a complete set of three mutually unbiased bases for a single qubit using two different IBM machines.
