宝石基体的量子测量与包结常数的相容性
Compatibility of quantum measurements and inclusion constants for the matrix jewel
摘要：
在这项工作中，我们建立了自由光谱面体的研究和量子测量与任意数量的结果的兼容性之间的联系。这概括了作者以前的两个结果的测量结果。自由谱面产生于线性矩阵不等式的矩阵松弛。一个特殊的自由spectrahedron，我们在这项工作中定义的矩阵宝石。我们发现，任意测量的兼容性对应于包含矩阵宝石到一个自由的spectrahedron定义的影响运营商的测量研究。随后，我们使用这种连接绑定的矩阵宝石使用结果从量子信息理论和对称化的（不对称）包含常数的集合。后者转化为量子测量兼容性的新下限。我们采用的技术包括近似量子克隆和互无偏基。
英文摘要：
In this work, we establish the connection between the study of free spectrahedra and the compatibility of quantum measurements with an arbitrary number of outcomes. This generalizes previous results by the authors for measurements with two outcomes. Free spectrahedra arise from matricial relaxations of linear matrix inequalities. A particular free spectrahedron which we define in this work is the matrix jewel. We find that the compatibility of arbitrary measurements corresponds to the inclusion of the matrix jewel into a free spectrahedron defined by the effect operators of the measurements under study. We subsequently use this connection to bound the set of (asymmetric) inclusion constants for the matrix jewel using results from quantum information theory and symmetrization. The latter translate to new lower bounds on the compatibility of quantum measurements. Among the techniques we employ are approximate quantum cloning and mutually unbiased bases.
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