论文标题
量子理论中的对角线统一和正交对称性
Diagonal unitary and orthogonal symmetries in quantum theory
论文作者
论文摘要
我们在对角线统一和正交组的作用下分别分析了基质代数之间的双分矩阵和线性图。通过介绍文献中广泛的示例列表，其中包括诸如对角线对称状态和Choi-Type地图之类的著名条目，我们表明，这类矩阵（和地图）涵盖了各种各样的场景，从而统一了他们的研究。我们检查了它们的线性代数结构，并通过凸圆锥体的表现研究了阳性的不同概念。特别是，我们将完全阳性矩阵的众所周知的锥体推广到三方向完全阳性矩阵的锥体，并将其连接到相关不变状态的可分离性（或相应量子通道的纠缠破坏特性）。对于线性地图，我们根据其Kraus，stinespring和Choi表示，提供了陈述协方差的明确特征，并系统地分析了阳性，可分解性，完全阳性等的常见属性。我们还描述了这些地图的不变子空间，并使用它们的结构来提供必要的条件，以使相关不变的两分状状态可分离性。
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the literature, which includes notable entries like the Diagonal Symmetric states and the Choi-type maps, we show that this class of matrices (and maps) encompasses a wide variety of scenarios, thereby unifying their study. We examine their linear algebraic structure and investigate different notions of positivity through their convex conic manifestations. In particular, we generalize the well-known cone of completely positive matrices to that of triplewise completely positive matrices and connect it to the separability of the relevant invariant states (or the entanglement breaking property of the corresponding quantum channels). For linear maps, we provide explicit characterizations of the stated covariance in terms of their Kraus, Stinespring, and Choi representations, and systematically analyze the usual properties of positivity, decomposability, complete positivity, and the like. We also describe the invariant subspaces of these maps and use their structure to provide necessary and sufficient conditions for separability of the associated invariant bipartite states.
