Compactly accessible categories and quantum key distribution

Details Compactly accessible categories and quantum key distribution Compactly accessible categories and quantum key distribution

2008-11-13

arxiv.org/abs/0811.2113v2

LMCS 4 (4:9) 2008

Computer Science

Logic in Computer Science

26 pages

Scientific paper

10.2168/LMCS-4(4:9)2008

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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