论文标题
一般概率理论，广义谱图和张量规范中的不兼容
Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms
论文作者
论文摘要
在这项工作中，我们研究了一般概率理论（GPT）中的测量不兼容。我们显示了兼容测量值的几种等效特征。首先是相关图的积极性。第二个与包含某些广义谱系的兼容性有关。为此，我们将自由谱的理论扩展到有序的向量空间。第三个表征将二分法测量值与Banach空间的张量跨诺植物的比率联系起来。我们使用这些特征来研究不同GPT（即它们的兼容区域）中存在的不兼容量。对于中央对称的GPT，我们表明兼容性程度为相关Banach空间的张量产品的注射量和投射标准的比率。这使我们能够完全表征几个GPT的兼容性区域，并根据相关Banach空间的1夏末常数获得兼容度的最佳通用界限。此外，我们在三个以上的量子测量值中发现了最大不相容性的新界限。
In this work, we investigate measurement incompatibility in general probabilistic theories (GPTs). We show several equivalent characterizations of compatible measurements. The first is in terms of the positivity of associated maps. The second relates compatibility to the inclusion of certain generalized spectrahedra. For this, we extend the theory of free spectrahedra to ordered vector spaces. The third characterization connects the compatibility of dichotomic measurements to the ratio of tensor crossnorms of Banach spaces. We use these characterizations to study the amount of incompatibility present in different GPTs, i.e. their compatibility regions. For centrally symmetric GPTs, we show that the compatibility degree is given as the ratio of the injective and the projective norm of the tensor product of associated Banach spaces. This allows us to completely characterize the compatibility regions of several GPTs, and to obtain optimal universal bounds on the compatibility degree in terms of the 1-summing constants of the associated Banach spaces. Moreover, we find new bounds on the maximal incompatibility present in more than three qubit measurements.
