Compactly accessible categories and quantum key distribution

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.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Chris Heunen
• Keywords: Accessible Category, Compact Categories, CORR 2008, Education, Quantum Key Distribution