Compactly Accessible Categories and Quantum Key Distribution
Compactly Accessible Categories and Quantum Key Distribution
复制标题
紧凑可访问的类别和量子密钥分配
DOI：
10.2168/lmcs-4(4:9)2008
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
C. Heunen
中科院分区：
文献类型：
--
作者：
C. Heunen
紧凑范畴最近通过在量子物理中的应用重新引起了人们的兴趣。由于本质上是有限维的，它们不能容纳(共同)基于限制的构造。例如，它们无法捕获依赖于大数定律的量子密钥分发等协议。为了克服这一限制，我们引入了紧凑可访问范畴的概念，依赖于因式分解系统的额外结构。这个概念允许无限维，同时保留紧范畴的关键性质：主要的技术结果是紧部分上的对偶选择函子规范地扩展到整个紧可达范畴。作为一个例子，我们建立了一个量子密钥分配协议的模型，并证明了它的正确性。
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum key distribution, that rely on the law of large numbers. To overcome this limitation, we introduce the notion of a compactly accessible category, relying on the extra structure of a factorisation system. This notion allows for infinite dimension while retaining key properties of compact categories: the main technical result is that the choice-of-duals functor on the compact part extends canonically to the whole compactly accessible category. As an example, we model a quantum key distribution protocol and prove its correctness categorically.