论文标题
量子超图的特征是当地
Quantum Supermaps are Characterized by Locality
论文作者
论文摘要
我们以公理的方式提供了量子超图的新表征，该公理仅是指顺序和平行组成。因此，我们将量子超图推广到任意的单体类别和操作概率理论。我们通过在单体类别上提供了对本地适用转换的简单定义来做到的。该定义可以使用自然原则以类别理论的语言来改写，并且可以在所有证据中给出直观的图表表示。在我们的主要技术贡献中，我们使用此图表表示，表明量子通道上的局部适用转换与确定性量子超级图的一对一对应。事实证明，量子超图的这种替代表征可用于更通用的多输入超图，例如量子开关和量子通道的任意正常凸空间，例如通过满足信号约束来定义的量子通道。
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational probabilistic theories. We do so by providing a simple definition of locally-applicable transformation on a monoidal category. The definition can be rephrased in the language of category theory using the principle of naturality, and can be given an intuitive diagrammatic representation in terms of which all proofs are presented. In our main technical contribution, we use this diagrammatic representation to show that locally-applicable transformations on quantum channels are in one-to-one correspondence with deterministic quantum supermaps. This alternative characterization of quantum supermaps is proven to work for more general multiple-input supermaps such as the quantum switch and on arbitrary normal convex spaces of quantum channels such as those defined by satisfaction of signaling constraints.
