Fetching the paper…
Reading the bibliography…
We show that Rob Spekken's toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category FRel of finite sets and relations with the cartesian product as tensor, where observables correspond to dagger Frobenius algebras.
S. MacLane (1998) Categories for the Working Mathematician. 2nd edition. Springer-Verlag
1998
Earlier work this paper cites.
S. Abramsky and B. Coecke (2004) A categorical semantics of quantum protocols. In: Proceedings of 19th IEEE conference on Logic in Computer Science, pages 415–425. IEEE Press. arXiv:quant-ph/0402130
2004
Earlier work this paper cites.
J. C. Baez (2006) Quantum quandaries: a category-theoretic perspective. In: The Structural Foundations of Quantum Gravity, D. Rickles, S. French and J. T. Saatsi (Eds), pages 240–266. Oxford University Press. arXiv:quant-ph/0404040
2006
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 categories and completely positive maps. Electronic Notes in Theoretical Computer Science
2007
Cited alongside, same era.
R. Spekkens (2007) Evidence for the epistemic view of quantum states: A toy theory. Physical Review A
2007
Cited alongside, same era.
R. Spekkens (2007) Axiomatization through foil theories. Talk, July 5, University of Cambridge
2007
Cited alongside, same era.
B. Coecke and R. W. Duncan (2008) Interacting quantum observables. In: Proceedings of the 35th International Colloquium on Automata, Languages and Programming, pages 298–310, Lecture Notes in Computer Science
2008
Closest in time.
B. Coecke, E. O. Paquette and D. Pavlovic (2007) Classical structures and quantum structures. In: Semantic Techniques in Quantum Computation, S. Gay and I. Mackie, Eds., Cambridge University Press, 2008. to appear
2008
Closest in time.
B. Coecke, D. Pavlovic, and J. Vicary (2008) Commutative dagger Frobenius algebras in
2008
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…