A Kochen-Specker system has at least 22 vectors (extended abstract)

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Sander Uijlen; Bas Westerbaan;

At the heart of the Conway-Kochen Free Will theorem and Kochen and Specker's argument against non- contextual hidden variable theories is the existence of a Kochen-Specker (KS) system: a set of points on the sphere that has no 0,1-coloring such that at most one of two o... View more
  • References (16)
    16 references, page 1 of 2

    [1] Felix Arends (2009): A Lower Bound on the Size of the Smallest Kochen-Specker Vector System in Three Dimensions. Master's thesis, University of Oxford. Available at http://www.cs.ox.ac.uk/people/ joel.ouaknine/download/arends09.pdf.

    [2] Felix Arends, Joe¨l Ouaknine & Charles W Wampler (2011): On searching for Small Kochen-Specker Vector Systems. In: Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science, Springer-Verlag, pp. 23-34, doi:10.1007/978-3-642-25870-1_4.

    [3] Ada´n Cabello (2000): Kochen-Specker theorem and experimental test on hidden variables. International Journal of Modern Physics A 15(18), pp. 2813-2820, doi:10.1016/S0217-751X(00)00202-9.

    [4] George E Collins (1998): Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Quantifier elimination and cylindrical algebraic decomposition, Springer, pp. 85-121, doi:10.1007/ 978-3-7091-9459-1_2.

    [5] John H Conway & Simon Kochen (2009): The strong free will theorem. Notices of the AMS 56(2), pp. 226-232.

    [6] Andreas Dolzmann & Thomas Sturm (1997): Redlog: Computer algebra meets computer logic. Acm Sigsam Bulletin 31(2), pp. 2-9, doi:10.1145/261320.261324.

    [7] Simon Kochen & EP Specker (1975): The problem of hidden variables in quantum mechanics. In: The Logico-Algebraic Approach to Quantum Mechanics, Springer, pp. 293-328, doi:10.1007/ 978-94-010-1795-4_17.

    [8] Brendan D McKay (1998): Isomorph-free exhaustive generation. Journal of Algorithms 26(2), pp. 306-324, doi:10.1006/jagm.1997.0898.

    [9] Joe¨l Ouaknine: personal communication. Attended such a lecture of Conway at the Oxford Mathematical Institute in 2005.

    [10] Asher Peres (1991): Two simple proofs of the Kochen-Specker theorem. Journal of Physics A: Mathematical and General 24(4), p. L175, doi:10.1088/0305-4470/24/4/003.

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