Compactly accessible categories and quantum key distribution Export

@article{citeulike:3517949, 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.}, archivePrefix = {arXiv}, author = {Heunen, Chris}, citeulike-article-id = {3517949}, citeulike-linkout-0 = {http://arxiv.org/abs/0811.2113}, citeulike-linkout-1 = {http://arxiv.org/pdf/0811.2113}, day = {13}, eprint = {0811.2113}, keywords = {category-theory, languages, logic, mathematics, quantum}, month = {Nov}, posted-at = {2008-11-15 02:30:58}, priority = {3}, title = {Compactly accessible categories and quantum key distribution}, url = {http://arxiv.org/abs/0811.2113}, year = {2008} }

TY - JOUR ID - citeulike:3517949 L3 - citeulike-article-id:3517949 N2 - 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. TI - Compactly accessible categories and quantum key distribution KW - category-theory KW - languages KW - logic KW - mathematics KW - quantum AU - Heunen, Chris PY - 2008/Nov/13/ UR - http://arxiv.org/abs/0811.2113 ER -