论文标题
自由多类，用于任意维度的统一超图
Free Polycategories for Unitary Supermaps of Arbitrary Dimension
论文作者
论文摘要
我们为孔提供了一个结构，可以插入抽象对称单体类别的形态，称为Polyslot Construction PSLOT [C]，并识别可代表单方面的Polyslots的子级SREP [C]。这些结构加强了先前引入的本地可应用转换的概念，该概念用于以一种足以直接从单位类别类型的单体结构重新构造单一超图的方式来表征量子超图。这两个结构还可以自由地重建量子超图的富集多分类语义，该语义允许序列和平行地组成超级图，同时禁止创建时间循环。通过自由构造超图像的关键组成特征，并在有限维情况下表征超图，提出了Polyslots作为对无限尺寸的合适概括性的概括，并被证明包括规范示例，例如量子开关。除了对量子相关类别的特定应用外，还定义了称为途径 - 收集组的一般分类结构，在该类别上，SREP [C]和PSLOT [C]构建体显示为重合。
We provide a construction for holes into which morphisms of abstract symmetric monoidal categories can be inserted, termed the polyslot construction pslot[C], and identify a sub-class srep[C] of polyslots that are single-party representable. These constructions strengthen a previously introduced notion of locally-applicable transformation used to characterize quantum supermaps in a way that is sufficient to re-construct unitary supermaps directly from the monoidal structure of the category of unitaries. Both constructions furthermore freely reconstruct the enriched polycategorical semantics for quantum supermaps which allows to compose supermaps in sequence and in parallel whilst forbidding the creation of time-loops. By freely constructing key compositional features of supermaps, and characterizing supermaps in the finite-dimensional case, polyslots are proposed as a suitable generalization of unitary-supermaps to infinite dimensions and are shown to include canonical examples such as the quantum switch. Beyond specific applications to quantum-relevant categories, a general class of categorical structures termed path-contraction groupoids are defined on which the srep[C] and pslot[C] constructions are shown to coincide.
