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arXiv · 0811.2113

Compactly accessible categories and quantum key distribution

Chris Heunen
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Abstract

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.

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Chris Heunen. 2008-11-13. Compactly accessible categories and quantum key distribution. https://doi.org/10.2168/lmcs-4(4:9)2008

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