论文标题
通过其Naimark扩展表征量子测量的不兼容
Characterizing incompatibility of quantum measurements via their Naimark extensions
论文作者
论文摘要
我们通过其Naimark扩展来获得一组正面操作员值措施（POVM）的兼容性或其他方式的形式表征。我们表明，只有在同一Ancilla Hilbert空间上的固定Ancilla状态指定的单个Naimark扩展时，只有存在单个Naimark扩展，将它们映射到一组通勤投影测量（PVM）时，我们才能共同测量一组POVM。我们使用我们的结果来获得易于检查的足够条件，以在任何维度中兼容一对二分法可观察物。反过来，这导致了一些重要类别的可观察到的兼容区域的表征，包括一对Unsharp Qubit可观察物。最后，我们还概述了我们的结果如何提供量化一般量子测量值不兼容的替代方法。
We obtain a formal characterization of the compatibility or otherwise of a set of positive-operator-valued measures (POVMs) via their Naimark extensions. We show that a set of POVMs is jointly measurable if and only if there exists a single Naimark extension, specified by a fixed ancilla state on the same ancilla Hilbert space, that maps them to a set of commuting projective measurements (PVMs). We use our result to obtain an easily checkable sufficient condition for the compatibility of a pair of dichotomic observables in any dimension. This in turn leads to a characterization of the compatibility regions for some important classes of observables including a pair of unsharp qubit observables. Finally, we also outline as to how our result provides an alternate approach to quantifying the incompatibility of a general set of quantum measurements.
