Quantum Logic in Dagger Kernel Categories

Article, Report, Preprint English OPEN
Heunen, Chris; Jacobs, Bart;
  • Publisher: s.n.
  • Journal: volume 27,issue 2,pages177-212issn: 0167-8094
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1007/s11083-010-9145-5, doi: 10.1016/j.entcs.2011.01.024
  • Subject: 03G12, 03G30 | Mathematics - Category Theory | Geometry and Topology | Mathematics - Logic | Orthomodular lattice | Computational Theory and Mathematics | Algebra and Number Theory | Quantum logic | Theoretical Computer Science | Computer Science(all) | Categorical logic | Dagger kernel category | Quantum Physics
    arxiv: Mathematics::Category Theory | Computer Science::Logic in Computer Science

This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categorie... View more
  • References (21)
    21 references, page 1 of 3

    [1] S. Abramsky and B. Coecke. A categorical semantics of quantum protocols. In Logic in Computer Science, pages 415-425. IEEE, Computer Science Press, 2004.

    [9] G.D. Crown. On some orthomodular posets of vector bundles. Journ. of Natural Sci. and Math., 15(1-2):11-25, 1975.

    [10] B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Math. Textbooks. Cambridge Univ. Press, 1990.

    [11] A. Dvureˇcenskij and S. Pulmannov´a. New Trends in Quantum Structures. Kluwer Acad. Publ., Dordrecht, 2000.

    [12] P. D. Finch. Quantum logic as an implication algebra. Bull. Amer. Math. Soc., 2:101-106, 1970.

    [13] D. J. Foulis, R.J. Greechie, and M.K. Bennett. Sums and products of interval algebras. Int. Journ. Theor. Physics, 33(11):2119-2136, 1994.

    [14] P.J. Freyd. Abelian Categories: An Introduction to the Theory of Functors. Harper and Row, New York, 1964. Available via www.tac.mta.ca/tac/reprints/articles/3/tr3.pdf.

    [15] E. Haghverdi and Ph. Scott. A categorical model for the geometry of interaction. Theor. Comp. Sci., 350:252-274, 2006.

    [16] J. Harding. Orthomodularity of decompositions in a categorical setting. Int. Journ. Theor. Physics, 45(6):1117-1128, 2006.

    [17] C. Heunen. Compactly accessible categories and quantum key distribution. Logical Methods in Comp. Sci., 4(4), 2008.

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