复合量子逻辑
Compositional Quantum Logic
摘要：
量子逻辑的目标是在序理论中捕获基本的量子力学结构。量子逻辑的阿喀琉斯之踵是缺乏对复合系统的规范描述，给出了对它们组成部分的描述。我们引入了一个框架，在该框架中，序理论结构与一个原始的组合操作。该命令是从适用于任意匕首对称monoidal类别的C*-代数的推广中提取的，它还提供了组合操作。事实上，我们的构造完全是合成的，没有任何关于极限或富集的额外假设。在有限维Hilbert空间范畴中得到任意有限维C*-代数的投影格。有趣的是，有一些模型伪造了标准假设的对应关系，最值得注意的是代数的非交换性和阶的非分配性之间的对应关系。
英文摘要：
Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We introduce a framework in which order-theoretic structure comes with a primitive composition operation. The order is extracted from a generalisation of C*-algebra that applies to arbitrary dagger symmetric monoidal categories, which also provide the composition operation. In fact, our construction is entirely compositional, without any additional assumptions on limits or enrichment. Interpreted in the category of finite-dimensional Hilbert spaces, it yields the projection lattices of arbitrary finite-dimensional C*-algebras. Interestingly, there are models that falsify standardly assumed correspondences, most notably the correspondence between noncommutativity of the algebra and nondistributivity of the order.
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