去线性化线性：强紧闭包的射影量子公理化
De-linearizing Linearity: Projective Quantum Axiomatics from Strong Compact Closure
摘要：
详细阐述我们与Abramsky在quant-ph/0402130中的联合工作，我们进一步将希尔伯特空间的线性结构分解为几个组成部分。有些证明是非常关键的特定功能的量子理论，而其他人阻碍通过的形式主义，这是不饱和的物理无关紧要的全球阶段。首先，我们表明，所需的线性结构的大部分是纯粹的乘法，并产生于强紧闭张量，除了提供各种概念，如标量，迹，酉性，自伴性和二分投影仪，还提供希尔伯特-施密特范数，希尔伯特-施密特内积，特别是，该公理使通道从形式主义的向量空间的一种相当投射的，因为它是打算在（中）著名的伯克霍夫和冯诺依曼文件。接下来，我们考虑分布在张量上的加法类型，从中可以构建测量，并且在quant-ph/0402130中讨论的协议的正确性证明可以延续到产生的较弱设置。一个完整的概率演算得到的轨迹是线性的，而且满足\em对角公理，这给我们带来了第二个主要结果，定性和定量有效的分类量子形式主义没有多余的全球阶段的必要和充分的添加剂结构的表征。一路上，我们表明，如果在一个类别（添加剂）monoidal张量分布在一个强紧闭张量，那么这个类别总是丰富的交换monoids。
英文摘要：
Elaborating on our joint work with Abramsky in quant-ph/0402130 we further unravel the linear structure of Hilbert spaces into several constituents. Some prove to be very crucial for particular features of quantum theory while others obstruct the passage to a formalism which is not saturated with physically insignificant global phases. First we show that the bulk of the required linear structure is purely multiplicative, and arises from the strongly compact closed tensor which, besides providing a variety of notions such as scalars, trace, unitarity, self-adjointness and bipartite projectors, also provides Hilbert-Schmidt norm, Hilbert-Schmidt inner-product, and in particular, the preparation-state agreement axiom which enables the passage from a formalism of the vector space kind to a rather projective one, as it was intended in the (in)famous Birkhoff & von Neumann paper. Next we consider additive types which distribute over the tensor, from which measurements can be build, and the correctness proofs of the protocols discussed in quant-ph/0402130 carry over to the resulting weaker setting. A full probabilistic calculus is obtained when the trace is moreover linear and satisfies the \em diagonal axiom, which brings us to a second main result, characterization of the necessary and sufficient additive structure of a both qualitatively and quantitatively effective categorical quantum formalism without redundant global phases. Along the way we show that if in a category a (additive) monoidal tensor distributes over a strongly compact closed tensor, then this category is always enriched in commutative monoids.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
