Chris Heunen - Compactly accessible categories and quantum key distribution

lmcs:1129 - Logical Methods in Computer Science, November 17, 2008, Volume 4, Issue 4 -
Compactly accessible categories and quantum key distribution

Authors: Chris Heunen

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.

Volume: Volume 4, Issue 4
Published on: November 17, 2008
Accepted on: June 25, 2015
Submitted on: October 30, 2007
Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages,Quantum Physics,F.3.2


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