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.
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.
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.
K. Cho, B. Jacobs, B. Westerbaan & A. Westerbaan (2015):
An introduction to effectus theory.
arXiv:1512.05813.
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.
B. Coecke & A. Kissinger (2017):
Picturing quantum processes.
Cambridge University Press,
doi:10.1017/9781316219317.
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.
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.
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.
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.
M. Giry (1980):
A categorical approach to probability theory.
Categorical aspects of topology and analysis 915,
pp. 68–85,
doi:10.1007/BFb0092872.
D. Gross (2006):
Hudson’s theorem for finite-dimensional quantum systems.
Journal of mathematical physics 47(12),
pp. 122107,
doi:10.1063/1.2393152.
S. Gudder (2009):
Quantum measure and integration theory.
Journal of Mathematical Physics 50,
pp. 123509,
doi:10.1063/1.3267867.
S. Gudder (2012):
Quantum measures and integrals.
Reports on Mathematical Physics 69(1),
pp. 87–101,
doi:10.1016/S0034-4877(12)60019-6.
C. Heunen & J. Vicary (2019):
Categories for quantum theory: an introduction.
Oxford University Press.
B. Jacobs (2013):
Measurable spaces and their effect logic.
In: Logic in Computer Science.
IEEE,
pp. 83–92,
doi:10.1109/LICS.2013.13.
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.
M. S. Leifer (2014):
Is the quantum state real?.
Quanta 3,
pp. 67–155,
doi:10.12743/quanta.v3i1.22.
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.
T. Leinster (2014):
Basic category theory.
Cambridge University Press,
doi:10.1017/CBO9781107360068.
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.
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.
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.
P. Panangaden (2009):
Labelled Markov processes.
World Scientific,
doi:10.1142/p595.
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.
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.
J. H. Selby, C. M. Scandolo & B. Coecke (2018):
Reconstructing quantum theory from diagrammatic postulates.
arXiv:1802.00367.
R. D. Sorkin (1994):
Quantum mechanics as quantum measure theory.
Modern Physics Letters A 9(33),
pp. 3119–3127,
doi:10.1142/S021773239400294X.
R. D. Sorkin (1995):
Quantum measure theory and its interpretation.
arXiv:gr-qc/9507057.
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.
Robert W Spekkens (2005):
Contextuality for preparations, transformations, and unsharp measurements.
Physical Review A 71(5),
pp. 052108,
doi:10.1103/PhysRevLett.92.127901.
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.
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.