论文标题
可积分的地图
Positively Factorizable Maps
论文作者
论文摘要
我们在$ m_n（\ mathbb {c}）上启动了一项线性地图的研究，该研究的属性是通过tracial von neumann algebra $（\ mathcal {\ mathcal {a，τ}）$ in oterator $ z \ in m_n（\ mathcal {a}）$组成的von-neceann cance的von n neumann algebra $（\ mathcal {a，τ}）$。这些地图通常是在非本地游戏的背景下出现的，尤其是在同步的情况下。我们在$ \ mathbb {r}^n $中建立了一个连接，其中包含自动锥和这些地图的存在。通过Abelian von-Neumann代数因素的choi矩阵被证明是一个完全正（CP）矩阵。 我们充分表征了可构化的地图，其CHOI等级为2。我们还提供了该分析的一些应用，以查找不是CPSD的双重非负矩阵。从量子信息理论中不可扩展的产品基础的概念中可以找到这些示例的特殊类别。
We initiate a study of linear maps on $M_n(\mathbb{C})$ that have the property that they factor through a tracial von Neumann algebra $(\mathcal{A,τ})$ via operators $Z\in M_n(\mathcal{A})$ whose entries consist of positive elements from the von-Neumann algebra. These maps often arise in the context of non-local games, especially in the synchronous case. We establish a connection with the convex sets in $\mathbb{R}^n$ containing self-dual cones and the existence of these maps. The Choi matrix of a map of this kind which factors through an abelian von-Neumann algebra turns out to be a completely positive (CP) matrix. We fully characterize positively factorizable maps whose Choi rank is 2. We also provide some applications of this analysis in finding doubly nonnegative matrices which are not CPSD. A special class of these examples is found from the concept of Unextendible Product Bases in quantum information theory.
