Compactly accessible categories and quantum key distribution
arXiv:0811.2113 · doi:10.2168/LMCS-4(4:9)2008
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.
26 pages in Logical Methods in Computer Science, Volume 4, Issue 4 (November 17, 2008) lmcs:1129