Built on

R. Penrose (1971) Applications of negative dimensional tensors. In: Combinatorial Mathematics and its Applications, D. Welsh (Ed), pages 221–244. Academic Press
1971
Earlier work this paper cites.
G. M. Kelly and M. L. Laplaza (1980) Coherence for compact closed categories. Journal of Pure and Applied Algebra
1980
Earlier work this paper cites.
R. W. Spekkens (2009) The power of epistemic restrictions in reconstructing quantum theory. Talk, August 10, Perimeter Institute. PRISA:09080009
Original
1980
Earlier work this paper cites.
A. Carboni and R. F. C. Walters (1987) Cartesian bicategories I. Journal of Pure and Applied Algebra
1987
Earlier work this paper cites.
A. Joyal and R. Street (1991) The Geometry of tensor calculus I. Advances in Mathematics
1991
Earlier work this paper cites.
S. Mac Lane (2000) Categories for the Working Mathematician (2nd edition), Springer-Verlag
2000
Earlier work this paper cites.
B. Coecke and D. Pavlovic (2007) Quantum measurements without sums. In: Mathematics of Quantum Computing and Technology, G. Chen, L. Kauffman and S. Lamonaco (eds), pages 567–604. Taylor and Francis. arXiv:quant-ph/0608035
2007
Earlier work this paper cites.
P. Selinger (2007) Dagger compact closed categories and completely positive maps. Electronic Notes in Theoretical Computer Science
2007
Earlier work this paper cites.

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D. Pavlovic (2009) Quantum and classical structures in nondeterminstic computation. Lecture Notes in Computer Science
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2009
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B. Coecke (2010) Quantum picturalism. Contemporary Physics
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2010
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B. Coecke, B. Edwards and R. W. Spekkens (2010) Phase groups and the origin of non-locality for qubits. Electronic Notes in Theoretical Computer Science
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2010
Later among the works it cites.
P. Selinger (2010) Autonomous categories in which
2010
Later among the works it cites.
B. Coecke and R. Duncan (2008) Interacting quantum observables. In: Proceedings of the 35th International Colloquium on Automata, Languages and Programming (ICALP), pages 298–310, Lecture Notes in Computer Science 5126, Springer-Verlag. Extended version (2011): Interacting quantum observables: categorical algebra and diagrammatics. New Journal of Physics

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2011

Spekkens's toy theory as a category of processes

Coecke, Bob, Edwards, Bill

Understand

We provide two mathematical descriptions of Spekkens's toy qubit theory, an inductively one in terms of a small set of generators, as well as an explicit closed form description.

It is a subcategory MSpek of the category of finite sets, relations and the cartesian product.
States of maximal knowledge form a subcategory Spek.
This establishes the consistency of the toy theory, which has previously only been constructed for at most four systems.

Built on

R. Penrose (1971) Applications of negative dimensional tensors. In: Combinatorial Mathematics and its Applications, D. Welsh (Ed), pages 221–244. Academic Press
1971
Earlier work this paper cites.
G. M. Kelly and M. L. Laplaza (1980) Coherence for compact closed categories. Journal of Pure and Applied Algebra
1980
Earlier work this paper cites.
R. W. Spekkens (2009) The power of epistemic restrictions in reconstructing quantum theory. Talk, August 10, Perimeter Institute. PRISA:09080009
Original
1980
Earlier work this paper cites.
A. Carboni and R. F. C. Walters (1987) Cartesian bicategories I. Journal of Pure and Applied Algebra
1987
Earlier work this paper cites.
A. Joyal and R. Street (1991) The Geometry of tensor calculus I. Advances in Mathematics
1991
Earlier work this paper cites.
S. Mac Lane (2000) Categories for the Working Mathematician (2nd edition), Springer-Verlag
2000
Earlier work this paper cites.
B. Coecke and D. Pavlovic (2007) Quantum measurements without sums. In: Mathematics of Quantum Computing and Technology, G. Chen, L. Kauffman and S. Lamonaco (eds), pages 567–604. Taylor and Francis. arXiv:quant-ph/0608035
2007
Earlier work this paper cites.
P. Selinger (2007) Dagger compact closed categories and completely positive maps. Electronic Notes in Theoretical Computer Science
2007
Earlier work this paper cites.