Classical Structures Based on Unitaries
Classical Structures Based on Unitaries
复制标题
基于酉元的经典结构
DOI：
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复制
发表时间：
2013
期刊：
影响因子：
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通讯作者：
P. Hines
中科院分区：
文献类型：
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作者：
P. Hines
从观察不同类别领域（逻辑和计算，与量子力学对比）中出现不同的复制概念开始，本文解决了它们何时或是否可能重合的问题。假设所有定义在绝对意义上都是严格的，我们表明情况永远不会如此。然而，允许定义公理采用规范同构，分类量子力学的经典结构与逻辑和计算模型中熟悉的自相似的分类属性之间的密切联系变得显而易见。
所需的规范同构是不平凡的，并且混合了类型化（多对象）和非类型化（单对象）张量和结构同构；我们给出的一致性结果证明了这种方法的合理性。
然后，我们给出一类示例，其中对象的不同自相似结构决定箭头的不同矩阵表示，就像经典结构决定希尔伯特空间中的矩阵表示一样。我们还给出了这种情况下线性代数中熟悉的概念的类似物，例如基的变化和对角化。
Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide. Provided all definitions are strict in the categorical sense, we show that this can never be the case. However, allowing for the defining axioms to be taken up to canonical isomorphism, a close connection between the classical structures of categorical quantum mechanics, and the categorical property of self-similarity familiar from logical and computational models becomes apparent.
The required canonical isomorphisms are non-trivial, and mix both typed (multi-object) and untyped (single-object) tensors and structural isomorphisms; we give coherence results that justify this approach.
We then give a class of examples where distinct self-similar structures at an object determine distinct matrix representations of arrows, in the same way as classical structures determine matrix representations in Hilbert space. We also give analogues of familiar notions from linear algebra in this setting such as changes of basis, and diagonalisation.
影响因子：
0.5
作者：
HINES P
通讯作者：
HINES P