The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Dagger Compact Closed Categories and Completely Positive Maps
Open accessAbstract
Dagger compact closed categories were recently introduced by Abramsky and Coecke, under the name “strongly compact closed categories”, as an axiomatic framework for quantum mechanics. We present a graphical language for dagger compact closed categories, and sketch a proof of its completeness for equational reasoning. We give a general construction, the CPM construction, which associates to each dagger compact closed category its “category of completely positive maps”, and we show that the resulting category is again dagger compact closed. We apply these ideas to Abramsky and Coecke's interpretation of quantum protocols, and to D'Hondt and Panangaden's predicate transformer semantics.
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Cites
Categories for the Working Mathematician
Lane, S. M. (1971) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-9839-7 · Cited by 8,817
Completely positive linear maps on complex matrices
Choi, M.-D. (1975) · Linear Algebra and its Applications · doi:10.1016/0024-3795(75)90075-0 · Cited by 2,659
The geometry of tensor calculus, I
Joyal, A., & Street, R. (1991) · Advances in Mathematics · doi:10.1016/0001-8708(91)90003-p · Cited by 660
Combinatorial Mathematics and Its Applications.
O., I. (1970) · Journal of the American Statistical Association · doi:10.2307/2284618 · Cited by 544
Towards a quantum programming language
SELINGER, P. (2004) · Mathematical Structures in Computer Science · doi:10.1017/s0960129504004256 · Cited by 480
Self-citationCoherence for compact closed categories
Kelly, G. M., & Laplaza, M. L. (1980) · Journal of Pure and Applied Algebra · doi:10.1016/0022-4049(80)90101-2 · Cited by 437
A Categorical Semantics of Quantum ProtocolsPreprint
Abramsky, S., & Coecke, B. (2004) · Cited by 415
D’Hondt, E., & Panangaden, P. (2006) · Mathematical Structures in Computer Science · doi:10.1017/s0960129506005251 · Cited by 158
Abramsky, S., & Duncan, R. (2004) · Cited by 76
Towards a semantics for higher-order quantum computation
Selinger, P. (2004) · Cited by 60
Self-citation
Cited by
Danos, V., Kashefi, E., & Panangaden, P. (2007) · Journal of the ACM · doi:10.1145/1219092.1219096 · Cited by 195
ZX-calculus for the working quantum computer scientist
van de Wetering, J. (2020) · arXiv · doi:10.48550/arxiv.2012.13966 · Cited by 68
Metadata
- Authors
- Selinger, P.
- Venue
- Electronic Notes in Theoretical Computer Science
- Publisher
- Elsevier BV
- Published
- 2007-03
- Volume
- 170
- Pages
- 139-163
- ISSN
- 1571-0661 (ISSN-L)
- OpenAlex
- W1982928587
- Cited by
- 390
- References
- 10
- FWCI
- 27.58
- Type
- journal article
- Language
- en
- Open access
- diamond
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