References

  1. Michael A. Arbib & Ernest G. Manes (1980): Partially additive categories and flow-diagram semantics. Journal of Algebra 62(1), pp. 203–227, doi:10.1016/0021-8693(80)90212-4.
  2. Howard Barnum, Jonathan Barrett, Lisa Orloff Clark, Matthew Leifer, Robert Spekkens, Nicholas Stepanik, Alex Wilce & Robin Wilke (2010): Entropy and information causality in general probabilistic theories. New Journal of Physics 12(3), doi:10.1088/1367-2630/12/3/033024.
  3. Howard Barnum & Alexander Wilce (2016): Post-Classical Probability Theory. In: G. Chiribella & R. W. Spekkens: Quantum Theory: Informational Foundations and Foils. Springer, pp. 367–420, doi:10.1007/978-94-017-7303-4_11.
  4. Jonathan Barrett (2007): Information processing in generalized probabilistic theories. Physical Review A 75(3), pp. 032304, doi:10.1103/PhysRevA.75.032304.
  5. Reinhard Börger & Ralf Kemper (1996): A cogenerator for preseparated superconvex spaces. Applied Categorical Structures 4(4), pp. 361–370, doi:10.1007/BF00122684.
  6. Gianni Cassinelli & Pekka Lahti (2016): An Axiomatic Basis for Quantum Mechanics. Foundations of Physics 46(10), pp. 1341–1373, doi:10.1007/s10701-016-0022-y.
  7. Giulio Chiribella, Giacomo Mauro D'Ariano & Paolo Perinotti (2015): Quantum from Principles. In: Quantum Theory: Informational Foundations and Foils. Springer, pp. 171–221, doi:10.1007/978-94-017-7303-4_6.
  8. Giulio Chiribella, Giacomo Mauro DAriano & Paolo Perinotti (2010): Probabilistic theories with purification. Physical Review A 81(6), pp. 062348, doi:10.1103/PhysRevA.81.062348.
  9. Kenta Cho (2015): Total and Partial Computation in Categorical Quantum Foundations. In: 12th International Workshop on Quantum Physics and Logic (QPL 2015), EPTCS 195, pp. 116–135, doi:10.4204/EPTCS.195.9.
  10. Kenta Cho (2019): Effectuses in Categorical Quantum Foundations. Radboud Unviersity Nijmegen. Available at http://hdl.handle.net/2066/207521.
  11. Kenta Cho, Bart Jacobs, Bas Westerbaan & Abraham Westerbaan (2015): An Introduction to Effectus Theory. arXiv preprint arXiv:1512.05813. Available at https://arxiv.org/abs/1512.05813.
  12. Giacomo Mauro D'Ariano, Giulio Chiribella & Paolo Perinotti (2017): Quantum Theory from First Principles: An Informational Approach. Cambridge University Press, doi:10.1017/9781107338340.
  13. E. B. Davies & J. T. Lewis (1970): An operational approach to quantum probability. Communications in Mathematical Physics 17(3), pp. 239–260, doi:10.1007/BF01647093.
  14. C. M. Edwards (1970): The operational approach to algebraic quantum theory I. Communications in Mathematical Physics 16(3), pp. 207–230, doi:10.1007/BF01646788.
  15. C. M. Edwards & M. A. Gerzon (1970): Monotone convergence in partially ordered vector spaces. Annales de l'I.H.P. Physique théorique 12(4), pp. 323–328. Available at http://www.numdam.org/item/AIHPA_1970__12_4_323_0.
  16. Pau Enrique Moliner, Chris Heunen & Sean Tull (2018): Space in Monoidal Categories. In: Bob Coecke & Aleks Kissinger: Proceedings 14th International Conference on Quantum Physics and Logic, Nijmegen, The Netherlands, 3-7 July 2017, Electronic Proceedings in Theoretical Computer Science 266. Open Publishing Association, pp. 399–410, doi:10.4204/EPTCS.266.25.
  17. David J Foulis & Mary K Bennett (1994): Effect algebras and unsharp quantum logics. Foundations of physics 24(10), pp. 1331–1352, doi:10.1007/BF02283036.
  18. David J. Foulis & Richard J. Greechie (2007): Quantum logic and partially ordered abelian groups. In: Handbook of Quantum Logic and Quantum Structures: Quantum Structures. Elsevier, pp. 215–283, doi:10.1016/B978-044452870-4/50028-5.
  19. Robert Furber (2017): Categorical Duality in Probability and Quantum Foundations. Radboud University Nijmegen. Available at http://hdl.handle.net/2066/175862.
  20. Robert Furber (2019): Categorical Equivalences from State-Effect Adjunctions. In: 15th International Conference on Quantum Physics and Logic (QPL 2018) 287, pp. 107–126, doi:10.4204/EPTCS.287.6.
  21. Leonard Gillman & Meyer Jerison (2013): Rings of continuous functions. Springer, doi:10.1007/978-1-4615-7819-2.
  22. Stanley Gudder (1998): Morphisms, tensor products and σ-effect algebras. Reports on Mathematical Physics 42(3), pp. 321–346, doi:10.1016/S0034-4877(99)80003-2.
  23. Stanley Gudder (1999): Convex structures and effect algebras. International Journal of Theoretical Physics 38(12), pp. 3179–3187, doi:10.1023/A:1026678114856.
  24. Stanley Gudder & Sylvia Pulmannová (1998): Representation theorem for convex effect algebras. Commentationes Mathematicae Universitatis Carolinae 39(4), pp. 645–660. Available at http://dml.cz/dmlcz/119041.
  25. John Harding (2004): Remarks on concrete orthomodular lattices. International Journal of Theoretical Physics 43(10), pp. 2149–2168, doi:10.1023/B:IJTP.0000049016.83846.72.
  26. Bart Jacobs (2011): Probabilities, distribution monads, and convex categories. Theoretical Computer Science 412(28), pp. 3323–3336, doi:10.1016/j.tcs.2011.04.005.
  27. Bart Jacobs (2015): New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic. Logical Methods in Computer Science 11(3), doi:10.2168/LMCS-11(3:24)2015.
  28. Bart Jacobs & Jorik Mandemaker (2012): Coreflections in algebraic quantum logic. Foundations of physics 42(7), pp. 932–958, doi:10.1007/s10701-012-9654-8.
  29. Bart Jacobs, Jorik Mandemaker & Robert Furber (2016): The expectation monad in quantum foundations. Information and Computation 250, pp. 87–114, doi:10.1016/j.ic.2016.02.009.
  30. Gejza Jenča (2015): Effect algebras are the Eilenberg-Moore category for the Kalmbach monad. Order 32(3), pp. 439–448, doi:10.1007/s11083-014-9344-6.
  31. Simon Kochen & E. P. Specker (1967): The Problem of Hidden Variables in Quantum Mechanics. Journal of Mathematics and Mechanics 17(1), pp. 59–87, doi:10.1512/iumj.1968.17.17004.
  32. Günther Ludwig (1983): Foundations of Quantum Mechanics I. Springer, doi:10.1007/978-3-642-86751-4.
  33. Günther Ludwig (1985): An Axiomatic Basis for Quantum Mechanics, Volume 1: Derivation of Hilbert Space Structure. Springer, doi:10.1007/978-3-642-70029-3.
  34. George W. Mackey (2004): Mathematical Foundations of Quantum Mechanics. Dover. Originally published by W. A. Benjamin, 1963.
  35. Ernest G. Manes & Michael A. Arbib (1986): Algebraic Approaches to Program Semantics. Monographs in Computer Science. Springer, doi:10.1007/978-1-4612-4962-7.
  36. Dieter Pumplün (2002): The Metric Completion of Convex Sets and Modules. Results in Mathematics 41, pp. 346–360, doi:10.1007/BF03322777.
  37. Sean Tull (2016): Operational theories of physics as categories. arXiv preprint arXiv:1602.06284. Available at https://arxiv.org/abs/1602.06284.
  38. Sean Tull (2018): Categorical Operational Physics. University of Oxford. Available at https://arxiv.org/abs/1902.00343.
  39. Abraham Westerbaan, Bas Westerbaan & John van de Wetering (2020): A Characterisation of Ordered Abstract Probabilities. In: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 20. Association for Computing Machinery, New York, NY, USA, pp. 944957, doi:10.1145/3373718.3394742.
  40. Bas Westerbaan (2018): Dagger and dilations in the category of von Neumann algebras. Radboud University Nijmegen. Available at http://hdl.handle.net/2066/201785.
  41. Bas E Westerbaan (2013): Sequential product on effect logics. Radboud University Nijmegen. Available at https://www.ru.nl/publish/pages/813276/masterscriptie_bas_westerbaan.pdf.
  42. J. D. Maitland Wright (1972): Measures with Values in a Partially Ordered Vector Space. Proceedings of the London Mathematical Society s3-25(4), pp. 675–688, doi:10.1112/plms/s3-25.4.675.
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