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Compactly accessible categories and quantum key distribution
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.Comment: 26 pages in Logical Methods in Computer Science, Volume 4, Issue 4
(November 17, 2008) lmcs:112