论文标题
高阶量子变换的射影表征
Projective characterization of higher-order quantum transformations
论文作者
论文摘要
转化的转换（也称为高阶变换）是信息处理中的自然概念，最近对量子因果关系的研究引起了重大兴趣。在这项工作中，提出了一个用于表征高阶量子变换的框架，该框架依赖于超级操作器投影仪的使用。更确切地说，与Choi-Jamiolkowski图片中的投影仪一起工作显示出一种方便的方式来定义任何高阶转换类别的表征约束。这些投影仪的代数特性也被确定为乘法添加线性逻辑（MALL）的模型。这项工作的主要新颖性是“ PREC”连接器代数的引言。它用于表征从输入到输出或相反方式的没有信号传导的地图。这允许评估投影框架内表征的任何地图的可能信号传导结构。此外，还显示了PREC的特性为投射表达式产生正常形式。这提供了一种系统的方法来比较不同类别的高阶转换类别。
Transformations of transformations, also called higher-order transformations, is a natural concept in information processing, which has recently attracted significant interest in the study of quantum causal relations. In this work, a framework for characterizing higher-order quantum transformations which relies on the use of superoperator projectors is presented. More precisely, working with projectors in the Choi-Jamiolkowski picture is shown to provide a handy way of defining the characterization constraints on any class of higher-order transformations. The algebraic properties of these projectors are furthermore identified as a model of multiplicative additive linear logic (MALL). The main novelty of this work is the introduction in the algebra of the 'prec' connector. It is used for the characterization of maps that are no signaling from input to output or the other way around. This allows to assess the possible signaling structure of any maps characterized within the projective framework. The properties of the prec are moreover shown to yield a normal form for projective expressions. This provides a systematic way to compare different classes of higher-order transformations.
