@article(aaronson2013psi, author = {S. Aaronson and A. Bouland and L. Chua and G. Lowther}, year = {2013}, title = {$\psi$-epistemic theories: The role of symmetry}, journal = {Physical Review A}, volume = {88}, number = {3}, pages = {032111}, doi = {10.1103/PhysRevA.88.032111}, ) @inproceedings(abramskyheunen:operational, author = {S. Abramsky and C. Heunen}, year = {2016}, title = {Operational theories and categorical quantum mechanics}, booktitle = {Logic and algebraic structures in quantum computing and information,}, series = {Lecture Notes in Logic}, volume = {45}, publisher = {Cambridge University Press}, pages = {88--122}, doi = {10.1017/CBO9781139519687.007}, ) @article(barnett2009quantum, author = {S. M. Barnett and S. Croke}, year = {2009}, title = {Quantum state discrimination}, journal = {Advances in Optics and Photonics}, volume = {1}, number = {2}, pages = {238--278}, doi = {10.1364/AOP.1.000238}, ) @article(bell1964einstein, author = {J. S. Bell}, year = {1964}, title = {On the {E}instein {P}odolsky {R}osen paradox}, journal = {Physics Physique Fizika}, volume = {1}, number = {3}, pages = {195}, doi = {10.1103/PhysicsPhysiqueFizika.1.195}, ) @article(jacobsetal:effectus, author = {K. Cho and B. Jacobs and B. Westerbaan and A. Westerbaan}, year = {2015}, title = {An introduction to effectus theory}, journal = {arXiv:1512.05813}, ) @article(coeckeheunenkissinger:cp, author = {B. Coecke and C. Heunen and A. Kissinger}, year = {2014}, title = {Categories of quantum and classical channels}, journal = {Quantum Information Processing}, pages = {1--31}, doi = {10.1007/s11128-014-0837-4}, ) @book(coeckekissinger, author = {B. Coecke and A. Kissinger}, year = {2017}, title = {Picturing quantum processes}, publisher = {Cambridge University Press}, doi = {10.1017/9781316219317}, ) @article(dowker2010hilbert, author = {F. Dowker and S. Johnston and R. D. Sorkin}, year = {2010}, title = {Hilbert spaces from path integrals}, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {43}, number = {27}, pages = {275302}, doi = {10.1088/1751-8113/43/27/275302}, ) @article(dowker2010extending, author = {F. Dowker and S. Johnston and S. Surya}, year = {2010}, title = {On extending the quantum measure}, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {43}, number = {50}, pages = {505305}, doi = {10.1088/1751-8113/43/50/505305}, ) @article(ferrie2011quasi, author = {C. Ferrie}, year = {2011}, title = {Quasi-probability representations of quantum theory with applications to quantum information science}, journal = {Reports on Progress in Physics}, volume = {74}, number = {11}, pages = {116001}, doi = {10.1088/0034-4885/74/11/116001}, ) @article(gibbons2004discrete, author = {K. S. Gibbons and M. J. Hoffman and W. K. Wootters}, year = {2004}, title = {Discrete phase space based on finite fields}, journal = {Physical Review A}, volume = {70}, number = {6}, pages = {062101}, doi = {10.1103/PhysRevA.70.062101}, ) @article(giry, author = {M. Giry}, year = {1980}, title = {A categorical approach to probability theory}, journal = {Categorical aspects of topology and analysis}, number = {915}, pages = {68--85}, doi = {10.1007/BFb0092872}, ) @article(gross2006hudson, author = {D. Gross}, year = {2006}, title = {Hudson’s theorem for finite-dimensional quantum systems}, journal = {Journal of mathematical physics}, volume = {47}, number = {12}, pages = {122107}, doi = {10.1063/1.2393152}, ) @article(gudder:integration, author = {S. Gudder}, year = {2009}, title = {Quantum measure and integration theory}, journal = {Journal of Mathematical Physics}, volume = {50}, pages = {123509}, doi = {10.1063/1.3267867}, ) @article(gudder:integrals, author = {S. Gudder}, year = {2012}, title = {Quantum measures and integrals}, journal = {Reports on Mathematical Physics}, volume = {69}, number = {1}, pages = {87--101}, doi = {10.1016/S0034-4877(12)60019-6}, ) @book(heunenvicary, author = {C. Heunen and J. Vicary}, year = {2019}, title = {Categories for quantum theory: an introduction}, publisher = {Oxford University Press}, ) @inproceedings(jacobs:measurableeffects, author = {B. Jacobs}, year = {2013}, title = {Measurable spaces and their effect logic}, booktitle = {Logic in Computer Science}, publisher = {IEEE}, pages = {83--92}, doi = {10.1109/LICS.2013.13}, ) @incollection(kochen1975problem, author = {S. Kochen and E. P. Specker}, year = {1975}, title = {The problem of hidden variables in quantum mechanics}, booktitle = {The logico-algebraic approach to quantum mechanics}, publisher = {Springer}, pages = {293--328}, doi = {10.1512/iumj.1968.17.17004}, ) @article(leifer:review, author = {M. S. Leifer}, year = {2014}, title = {Is the quantum state real?}, journal = {Quanta}, volume = {3}, pages = {67--155}, doi = {10.12743/quanta.v3i1.22}, ) @article(leifer2013maximally, author = {M. S. Leifer and O. J. E. Maroney}, year = {2013}, title = {Maximally epistemic interpretations of the quantum state and contextuality}, journal = {Physical review letters}, volume = {110}, number = {12}, pages = {120401}, doi = {10.1103/PhysRevLett.110.120401}, ) @book(leinster:categorytheory, author = {T. Leinster}, year = {2014}, title = {Basic category theory}, publisher = {Cambridge University Press}, doi = {10.1017/CBO9781107360068}, ) @article(lewis2012distinct, author = {P. G. Lewis and D. Jennings and J. Barrett and T. Rudolph}, year = {2012}, title = {Distinct quantum states can be compatible with a single state of reality}, journal = {Physical review letters}, volume = {109}, number = {15}, pages = {150404}, doi = {10.1103/PhysRevLett.109.150404}, ) @article(martin2005random, author = {X. Martin and D. {O’Connor} and R. D. Sorkin}, year = {2005}, title = {Random walk in generalized quantum theory}, journal = {Physical Review D}, volume = {71}, number = {2}, pages = {024029}, doi = {10.1103/PhysRevD.71.024029}, ) @inproceedings(panangaden:srel, author = {P. Panangaden}, year = {1998}, title = {The category of {M}arkov kernels}, booktitle = {Probabilistic Methods in Verification}, series = {Electronic Notes in Theoretical Computer Science}, volume = {22}, pages = {171--187}, doi = {10.1016/S1571-0661(05)80602-4}, ) @book(panangaden:labelledmarkovprocesses, author = {P. Panangaden}, year = {2009}, title = {Labelled {M}arkov processes}, publisher = {World Scientific}, doi = {10.1142/p595}, ) @article(puseybarrettrudolph:reality, author = {M. F. Pusey and J. Barrett and T. Rudolph}, year = {2012}, title = {On the reality of the quantum state}, journal = {Nature Physics}, volume = {8}, pages = {475--478}, doi = {10.1038/nphys2309}, ) @article(salgado2002some, author = {R. B. Salgado}, year = {2002}, title = {Some identities for the quantum measure and its generalizations}, journal = {Modern Physics Letters A}, volume = {17}, number = {12}, pages = {711--728}, doi = {10.1142/S0217732302007041}, ) @article(selbyscandolocoecke:reconstructing, author = {J. H. Selby and C. M. Scandolo and B. Coecke}, year = {2018}, title = {Reconstructing quantum theory from diagrammatic postulates}, journal = {arXiv:1802.00367}, ) @article(sorkin1994quantum, author = {R. D. Sorkin}, year = {1994}, title = {Quantum mechanics as quantum measure theory}, journal = {Modern Physics Letters A}, volume = {9}, number = {33}, pages = {3119--3127}, doi = {10.1142/S021773239400294X}, ) @article(sorkin1995quantum, author = {R. D. Sorkin}, year = {1995}, title = {Quantum measure theory and its interpretation}, journal = {arXiv:gr-qc/9507057}, ) @article(spekkens2007evidence, author = {R. W. Spekkens}, year = {2007}, title = {Evidence for the epistemic view of quantum states: A toy theory}, journal = {Physical Review A}, volume = {75}, number = {3}, pages = {032110}, doi = {10.1103/PhysRevA.75.032110}, ) @article(spekkens2005contextuality, author = {Robert W Spekkens}, year = {2005}, title = {Contextuality for preparations, transformations, and unsharp measurements}, journal = {Physical Review A}, volume = {71}, number = {5}, pages = {052108}, doi = {10.1103/PhysRevLett.92.127901}, ) @article(surya2010quantum, author = {S. Surya and P. Wallden}, year = {2010}, title = {Quantum covers in quantum measure theory}, journal = {Foundations of Physics}, volume = {40}, number = {6}, pages = {585--606}, doi = {10.1007/s10701-010-9419-1}, ) @article(van2017quantum, author = {John van de Wetering}, year = {2018}, title = {Quantum Theory is a Quasi-stochastic Process Theory}, journal = {Electronic Proceedings in Theoretical Computer Science}, volume = {266}, pages = {179–196}, doi = {10.4204/eptcs.266.12}, ) @article(PhysRev.40.749, author = {E. Wigner}, year = {1932}, title = {On the Quantum Correction For Thermodynamic Equilibrium}, journal = {Phys. Rev.}, volume = {40}, pages = {749--759}, doi = {10.1103/PhysRev.40.749}, url = {https://link.aps.org/doi/10.1103/PhysRev.40.749}, )