References

  1. S. Aaronson, A. Bouland, L. Chua & G. Lowther (2013): ψ-epistemic theories: The role of symmetry. Physical Review A 88(3), pp. 032111, doi:10.1103/PhysRevA.88.032111.
  2. S. Abramsky & C. Heunen (2016): Operational theories and categorical quantum mechanics. In: Logic and algebraic structures in quantum computing and information,, Lecture Notes in Logic 45. Cambridge University Press, pp. 88–122, doi:10.1017/CBO9781139519687.007.
  3. S. M. Barnett & S. Croke (2009): Quantum state discrimination. Advances in Optics and Photonics 1(2), pp. 238–278, doi:10.1364/AOP.1.000238.
  4. J. S. Bell (1964): On the Einstein Podolsky Rosen paradox. Physics Physique Fizika 1(3), pp. 195, doi:10.1103/PhysicsPhysiqueFizika.1.195.
  5. K. Cho, B. Jacobs, B. Westerbaan & A. Westerbaan (2015): An introduction to effectus theory. arXiv:1512.05813.
  6. B. Coecke, C. Heunen & A. Kissinger (2014): Categories of quantum and classical channels. Quantum Information Processing, pp. 1–31, doi:10.1007/s11128-014-0837-4.
  7. B. Coecke & A. Kissinger (2017): Picturing quantum processes. Cambridge University Press, doi:10.1017/9781316219317.
  8. F. Dowker, S. Johnston & R. D. Sorkin (2010): Hilbert spaces from path integrals. Journal of Physics A: Mathematical and Theoretical 43(27), pp. 275302, doi:10.1088/1751-8113/43/27/275302.
  9. F. Dowker, S. Johnston & S. Surya (2010): On extending the quantum measure. Journal of Physics A: Mathematical and Theoretical 43(50), pp. 505305, doi:10.1088/1751-8113/43/50/505305.
  10. C. Ferrie (2011): Quasi-probability representations of quantum theory with applications to quantum information science. Reports on Progress in Physics 74(11), pp. 116001, doi:10.1088/0034-4885/74/11/116001.
  11. K. S. Gibbons, M. J. Hoffman & W. K. Wootters (2004): Discrete phase space based on finite fields. Physical Review A 70(6), pp. 062101, doi:10.1103/PhysRevA.70.062101.
  12. M. Giry (1980): A categorical approach to probability theory. Categorical aspects of topology and analysis 915, pp. 68–85, doi:10.1007/BFb0092872.
  13. D. Gross (2006): Hudson’s theorem for finite-dimensional quantum systems. Journal of mathematical physics 47(12), pp. 122107, doi:10.1063/1.2393152.
  14. S. Gudder (2009): Quantum measure and integration theory. Journal of Mathematical Physics 50, pp. 123509, doi:10.1063/1.3267867.
  15. S. Gudder (2012): Quantum measures and integrals. Reports on Mathematical Physics 69(1), pp. 87–101, doi:10.1016/S0034-4877(12)60019-6.
  16. C. Heunen & J. Vicary (2019): Categories for quantum theory: an introduction. Oxford University Press.
  17. B. Jacobs (2013): Measurable spaces and their effect logic. In: Logic in Computer Science. IEEE, pp. 83–92, doi:10.1109/LICS.2013.13.
  18. S. Kochen & E. P. Specker (1975): The problem of hidden variables in quantum mechanics. In: The logico-algebraic approach to quantum mechanics. Springer, pp. 293–328, doi:10.1512/iumj.1968.17.17004.
  19. M. S. Leifer (2014): Is the quantum state real?. Quanta 3, pp. 67–155, doi:10.12743/quanta.v3i1.22.
  20. M. S. Leifer & O. J. E. Maroney (2013): Maximally epistemic interpretations of the quantum state and contextuality. Physical review letters 110(12), pp. 120401, doi:10.1103/PhysRevLett.110.120401.
  21. T. Leinster (2014): Basic category theory. Cambridge University Press, doi:10.1017/CBO9781107360068.
  22. P. G. Lewis, D. Jennings, J. Barrett & T. Rudolph (2012): Distinct quantum states can be compatible with a single state of reality. Physical review letters 109(15), pp. 150404, doi:10.1103/PhysRevLett.109.150404.
  23. X. Martin, D. O’Connor & R. D. Sorkin (2005): Random walk in generalized quantum theory. Physical Review D 71(2), pp. 024029, doi:10.1103/PhysRevD.71.024029.
  24. P. Panangaden (1998): The category of Markov kernels. In: Probabilistic Methods in Verification, Electronic Notes in Theoretical Computer Science 22, pp. 171–187, doi:10.1016/S1571-0661(05)80602-4.
  25. P. Panangaden (2009): Labelled Markov processes. World Scientific, doi:10.1142/p595.
  26. M. F. Pusey, J. Barrett & T. Rudolph (2012): On the reality of the quantum state. Nature Physics 8, pp. 475–478, doi:10.1038/nphys2309.
  27. R. B. Salgado (2002): Some identities for the quantum measure and its generalizations. Modern Physics Letters A 17(12), pp. 711–728, doi:10.1142/S0217732302007041.
  28. J. H. Selby, C. M. Scandolo & B. Coecke (2018): Reconstructing quantum theory from diagrammatic postulates. arXiv:1802.00367.
  29. R. D. Sorkin (1994): Quantum mechanics as quantum measure theory. Modern Physics Letters A 9(33), pp. 3119–3127, doi:10.1142/S021773239400294X.
  30. R. D. Sorkin (1995): Quantum measure theory and its interpretation. arXiv:gr-qc/9507057.
  31. R. W. Spekkens (2007): Evidence for the epistemic view of quantum states: A toy theory. Physical Review A 75(3), pp. 032110, doi:10.1103/PhysRevA.75.032110.
  32. Robert W Spekkens (2005): Contextuality for preparations, transformations, and unsharp measurements. Physical Review A 71(5), pp. 052108, doi:10.1103/PhysRevLett.92.127901.
  33. S. Surya & P. Wallden (2010): Quantum covers in quantum measure theory. Foundations of Physics 40(6), pp. 585–606, doi:10.1007/s10701-010-9419-1.
  34. John van de Wetering (2018): Quantum Theory is a Quasi-stochastic Process Theory. Electronic Proceedings in Theoretical Computer Science 266, pp. 179–196, doi:10.4204/eptcs.266.12.
  35. E. Wigner (1932): On the Quantum Correction For Thermodynamic Equilibrium. Phys. Rev. 40, pp. 749–759, doi:10.1103/PhysRev.40.749. Available at https://link.aps.org/doi/10.1103/PhysRev.40.749.

Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org