Built on

R. Penrose (1971) Applications of negative dimensional tensors. In: Combinatorial Mathematics and its Applications, 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.
D. M. Greenberger, M. A. Horne, A. Shimony and A. Zeilinger (1990) Bell’s theorem without inequalities. American Journal of Physics
1990
Earlier work this paper cites.
N. D. Mermin (1990) Quantum mysteries revisited. American Journal of Physics
1990
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A. Joyal and R. Street (1991) The Geometry of tensor calculus I. Advances in Mathematics
1991
Earlier work this paper cites.
S. MacLane (1998) Categories for the Working Mathematician. 2nd edition. Springer-Verlag
1998
Earlier work this paper cites.
J. Kock (2003) Frobenius Algebras and 2D Topological Quantum Field Theories. Cambridge University Press
2003
Earlier work this paper cites.
S. Lack (2004) Composing PROPs. Theory and Applications of Categories
2004
Earlier work this paper cites.
B. Coecke (2006) Introducing categories to the practicing physicist. In: What is Category Theory? pages 45–74. Advanced Studies in Mathematics and Logic
Original
2006
Earlier work this paper cites.

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B. Coecke and E. O. Paquette (2006) POVMs and Naimark’s theorem without sums. Electronic Notes in Theoretical Computer Science
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2007
Cited alongside, same era.
P. Selinger (2007) Dagger compact categories and completely positive maps. Electronic Notes in Theoretical Computer Science
2007

Then

B. Coecke, D. Pavlovic, and J. Vicary (2008) A new description of orthogonal bases. arXiv:0810.0812
Original
2008
Later among the works it cites.
D. Pavlovic (2008) Quantum and classical structures in nondeterminstic computation. Lecture Notes in Computer Science
Original
2008
Later among the works it cites.
R. W. Spekkens and O. Schreiber (2008) The power of epistemic restrictions in axiomatizing quantum theory: from trits to qutrits. Talk, July 17, University of Oxford. categorieslogicphysics.wikidot.com/ people
Original
2008
Later among the works it 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. Revised version (2009): Categorical quantum mechanics. In: Handbook of Quantum Logic and Quantum Structures, K. Engesser, D. M. Gabbay and D. Lehmann (eds), pages 261–323. Elsevier. arXiv:0808.1023
Original
2009
Later among the works it cites.

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2010

Phase groups and the origin of non-locality for qubits

Coecke, Bob, Edwards, Bill, Spekkens, Robert W.

Understand

We describe a general framework in which we can precisely compare the structures of quantum-like theories which may initially be formulated in quite different mathematical terms.

We then use this framework to compare two theories: quantum mechanics restricted to qubit stabiliser states and operations, and Spekkens's toy theory.
We discover that viewed within our framework these theories are very similar, but differ in one key aspect - a four element group we term the phase group which emerges naturally within our framework.
In the case of the stabiliser theory this group is Z4 while for Spekkens's toy theory the group is Z2 x Z2.

Built on

R. Penrose (1971) Applications of negative dimensional tensors. In: Combinatorial Mathematics and its Applications, 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.
D. M. Greenberger, M. A. Horne, A. Shimony and A. Zeilinger (1990) Bell’s theorem without inequalities. American Journal of Physics
1990
Earlier work this paper cites.
N. D. Mermin (1990) Quantum mysteries revisited. American Journal of Physics
1990
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. MacLane (1998) Categories for the Working Mathematician. 2nd edition. Springer-Verlag
1998
Earlier work this paper cites.
J. Kock (2003) Frobenius Algebras and 2D Topological Quantum Field Theories. Cambridge University Press
2003
Earlier work this paper cites.
S. Lack (2004) Composing PROPs. Theory and Applications of Categories
2004
Earlier work this paper cites.
B. Coecke (2006) Introducing categories to the practicing physicist. In: What is Category Theory? pages 45–74. Advanced Studies in Mathematics and Logic
Original
2006
Earlier work this paper cites.

Similar

B. Coecke and E. O. Paquette (2006) POVMs and Naimark’s theorem without sums. Electronic Notes in Theoretical Computer Science
2006
Cited alongside, same era.
J. Barrett (2007) Information processing in generalized probabilistic theories. Physical Review A
2007
Cited alongside, same era.
B. Coecke (2007) De-linearizing linearity: projective quantum axiomatics from strong compact closure. Electronic Notes in Theoretical Computer Science
2007
Cited alongside, same era.
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
Cited alongside, same era.
P. Selinger (2007) Dagger compact categories and completely positive maps. Electronic Notes in Theoretical Computer Science
2007

Then

B. Coecke, D. Pavlovic, and J. Vicary (2008) A new description of orthogonal bases. arXiv:0810.0812
Original
2008
Later among the works it cites.
D. Pavlovic (2008) Quantum and classical structures in nondeterminstic computation. Lecture Notes in Computer Science
Original
2008
Later among the works it cites.
R. W. Spekkens and O. Schreiber (2008) The power of epistemic restrictions in axiomatizing quantum theory: from trits to qutrits. Talk, July 17, University of Oxford. categorieslogicphysics.wikidot.com/ people
Original
2008
Later among the works it 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. Revised version (2009): Categorical quantum mechanics. In: Handbook of Quantum Logic and Quantum Structures, K. Engesser, D. M. Gabbay and D. Lehmann (eds), pages 261–323. Elsevier. arXiv:0808.1023
Original
2009
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

R. W. Spekkens (2007) Evidence for the epistemic view of quantum states: A toy theory. Physical Review A

2007

Cited alongside, same era.

H. Barnum, J. Barrett, M. Leifer and A. Wilce, Teleportation in general probabilistic theories, in Proceedings of the Clifford Lectures, Tulane University, March 12-15, 2008, to appear in

Original

2008

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

Original

2008

Cited alongside, same era.

B. Coecke and B. Edwards (2008) Toy quantum categories. Electronic Notes in Theoretical Computer Science, to appear. arXiv:0808.1037

Original

2008

Cited alongside, same era.

S. Abramsky and N. Tzevelekos (2009) Introduction to categories and categorical logic. In: New Structures for Physics, B. Coecke (ed), pages 3–89. Lecture Notes in Physics. Springer-Verlag

2009

Later among the works it cites.

J. Baez and M. Stay (2009) Physics, topology, logic and computation: a Rosetta Stone. In: New Structures for Physics, B. Coecke (ed), pages 91–166. Lecture Notes in Physics. Springer-Verlag. arXiv:0903.0340

Original

2009

Later among the works it cites.

B. Coecke and E. O. Paquette (2009) Categories for the practicing physicist. In: New Structures for Physics, B. Coecke (ed), pages 167–271. Lecture Notes in Physics, Springer-Verlag. arXiv:0905.3010

Original

2009

Later among the works it cites.

P. Selinger (2009) A survey of graphical languages for monoidal categories. In: New Structures for Physics, B. Coecke (ed), pages 275–337. Lecture Notes in Physics, Springer-Verlag. arXiv:0908.3347

Original

2009

Later among the works it cites.