论文标题
$ j $ - 州和无限度量空间之间的量子通道
$J$-states and quantum channels between indefinite metric spaces
论文作者
论文摘要
在目前的工作中，我们介绍并研究了配备不确定度量的空间上的状态和量子通道的概念。仅仅是我们将分析限制为临床框架。如下所示，从我们的研究中，可以发现，在以无限期度量的方式传递到空间时，在构建状态和量子通道的构建中需要使用矩阵相对于不确定度量的矩阵的使用；这阻止我们将某些顺序矩阵的空间$ m_ {n}（\ mathbb {c}）$作为$ c^{\ ast} $ - algebra。在我们的情况下，通过$ j $ - metric来定义此伴随，其中矩阵$ j $是$ m_ {n}（\ m athbb {c}）$的基本对称性。在我们的论文中，对于量子操作员，我们包括一般设置，这些操作员映射$ j_ {1} $ - 状态为$ j_ {2} $ - 状态，其中$ j_ {2} \ neq \ neq \ neq \ pm j_ {1} $是两个任意的基本符号。在该程序的中间，我们通过考虑$ \ Mathbb {C}^{n} $上的两个不同的无限度指标，对两个不同的矩阵空间之间的完全正面地图进行了研究。
In the present work, we introduce and study the concepts of state and quantum channel on spaces equipped with an indefinite metric. Exclusively, we will limit our analysis to the matricial framework. As it will be confirmed below, from our research it is noticed that, when passing to the spaces with indefinite metric, the use of the adjoint of a matrix with respect to the indefinite metric is required in the construction of states and quantum channels; which prevents us to consider the space of matrices of certain order $M_{n}(\mathbb{C})$ as a $C^{\ast}$-algebra. In our case, this adjoint is defined through a $J$-metric, where the matrix $J$ is a fundamental symmetry of $M_{n}(\mathbb{C})$. In our paper, for quantum operators, we include the general setting in the which, these operators map $J_{1}$-states into $J_{2}$-states, where $J_{2}\neq \pm J_{1}$ are two arbitrary fundamental symmetries. In the middle of this program, we carry out a study of the completely positive maps between two different positive matrices spaces by considering two different indefinite metrics on $\mathbb{C}^{n}$.
