Compactly accessible categories and quantum key distribution

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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.
Original languageEnglish
Pages (from-to)1-26
Number of pages26
JournalLogical Methods in Computer Science
Volume4
Issue number4
DOIs
Publication statusPublished - 17 Nov 2008

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