Quantum contextuality as a topological property, and the ontology of potentiality

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Published: Dec 29, 2020
Keywords:
quantum contextuality the Bell–Kochen–Specker Theorem quantum ontology potentiality ontic indefiniteness sheaf theory

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Marek Woszczek
Adam Mickiewicz University in Poznań
https://orcid.org/0000-0003-3833-5001

Abstract

Quantum contextuality and its ontological meaning are very controversial issues, and they relate to other problems concerning the foundations of quantum theory. I address this controversy and stress the fact that contextuality is a universal topological property of quantum processes, which conflicts with the basic metaphysical assumption of the definiteness of being. I discuss the consequences of this fact and argue that generic quantum potentiality as a real physical indefiniteness has nothing in common with the classical notions of possibility and counterfactuality, and that also it reverses, in a way, the classical mirror-like relation between actuality and definite possibility.

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Woszczek, M. (2020). Quantum contextuality as a topological property, and the ontology of potentiality. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (69), 145–189. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/504
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No. 69 (2020): Is logic a physical variable?
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References

Abbott, A.A., Calude, C.S. and Svozil, K., 2014. Value-indefinite observables are almost everywhere. Physical Review A [Online], 89(3), p.032109. Available at: https://doi.org/10.1103/PhysRevA.89.032109 [visited on 24 November 2020].

Abramsky, S. and Brandenburger, A., 2011. The sheaf-theoretic structure of non-locality and contextuality. New Journal of Physics [Online], 13(11), p.113036. Available at: https://doi.org/10.1088/1367-2630/13/11/113036 [visited on 24 November 2020].

Acín, A., Fritz, T., Leverrier, A. and Sainz, A.B., 2015. A combinatorial approach to nonlocality and contextuality. Communications in Mathematical Physics [Online], 334(2), pp.533–628. Available at: https://doi.org/10.1007/s00220-014-2260-1 [visited on 24 November 2020].

Ahrens, J., Amselem, E., Cabello, A. and Bourennane, M., 2013. Two fundamental experimental tests of nonclassicality with qutrits. Scientific Reports [Online], 3(1), p.2170. Available at: https://doi.org/10.1038/srep02170 [visited on 24 November 2020].

Akiba, K., 2004. Vagueness in the world. Noűs [Online], 38(3), pp.407–429. Available at: <https://www.jstor.org/stable/3506246> [visited on 24 November 2020].

Amselem, E., Rĺdmark, M., Bourennane, M. and Cabello, A., 2009. State-independent quantum contextuality with single photons. Physical Review Letters [Online], 103(16), p.160405. Available at: https://doi.org/10.1103/PhysRevLett.103.160405 [visited on 24 November 2020].

Aolita, L. et al., 2012. Fully nonlocal quantum correlations. Physical Review A [Online], 85(3), p.032107. Available at: https://doi.org/10.1103/PhysRevA.85.032107 [visited on 24 November 2020].

Barnes, E. and Williams, J.R.G., 2011. A theory of metaphysical indeterminacy. In: K. Bennett and D.W. Zimmerman, eds. Oxford Studies in Metaphysics. Vol. 6 [Online]. Oxford: Oxford University Press, pp.103–148. Available at: https://doi.org/10.1093/acprof:oso/9780199603039.003.0003 [visited on 24 November 2020].

Barnum, H. et al., 2000. Quantum probability from decision theory? Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences [Online], 456(1997), pp.1175–1182. Available at: https://doi.org/10.1098/rspa.2000.0557 [visited on 24 November 2020].

Barrett, J., Cavalcanti, E.G., Lal, R. and Maroney, O.J.E., 2014. No ψ-epistemic model can fully explain the indistinguishability of quantum states. Physical Review Letters [Online], 112(25), p.250403. Available at: https://doi.org/10.1103/PhysRevLett.112.250403 [visited on 24 November 2020].

Bartlett, S.D., Rudolph, T. and Spekkens, R.W., 2012. Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction. Physical Review A [Online], 86(1), p.012103. Available at: https://doi.org/10.1103/PhysRevA.86.012103 [visited on 24 November 2020].

Bartosik, H. et al., 2009. Experimental test of quantum contextuality in neutron interferometry. Physical Review Letters [Online], 103(4), p.040403. Available at: https://doi.org/10.1103/PhysRevLett.103.040403 [visited on 24 November 2020].

Bell, J.S., 1964. On the Einstein-Podolsky-Rosen paradox. Physics, 1, pp.195–200.

Bell, J.S., 1966. On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38(3), pp.447–452.

Bell, J.S., 1981. Bertlmann’s socks and the nature of reality. Le Journal de Physique Colloques [Online], 42(C2), pp.C2–41–C2–62. Available at: https://doi.org/10.1051/jphyscol:1981202 [visited on 24 November 2020].

Bella, S., 2005. The Science of the Individual: Leibniz’s Ontology of Individual Substance [Online], Topoi Library. Dordrecht: Springer. Available at: https://doi.org/10.1007/1-4020-3260-9.

Bermejo-Vega, J. et al., 2017. Contextuality as a resource for models of quantum computation with qubits. Physical Review Letters [Online], 119(12), p.120505. Available at: https://doi.org/10.1103/PhysRevLett.119.120505 [visited on 24 November 2020].

Bohr, N., 1935. Can quantum-mechanical description of physical reality be considered complete? Physical Review [Online], 48(8), pp.696–702. Available at: https://doi.org/10.1103/PhysRev.48.696 [visited on 24 November 2020].

Borges, G. et al., 2014. Quantum contextuality in a Young-type interference experiment. Physical Review A [Online], 89(5), p.052106. Available at: https://doi.org/10.1103/PhysRevA.89.052106 [visited on 24 November 2020].

Branciard, C., 2014. How ψ-epistemic models fail at explaining the indistinguishability of quantum states. Physical Review Letters [Online], 113, p.020409. Available at: https://doi.org/10.1103/PhysRevLett.113.020409 [visited on 24 November 2020].

Bruss, D., D’Ariano, G.M., Macchiavello, C. and Sacchi, M.F., 2000. Approximate quantum cloning and the impossibility of superluminal information transfer. Physical Review A [Online], 62(6), p.062302. Available at: https://doi.org/10.1103/PhysRevA.62.062302 [visited on 24 November 2020].

Bub, J., 2014. Quantum correlations and the measurement problem. International Journal of Theoretical Physics [Online], 53, pp.3346–3369. Available at: https://doi.org/10.1007/s10773-013-1695-z [visited on 24 November 2020].

Cabello, A., 1999a. Quantum correlations are not contained in the initial state. Physical Review A [Online], 60(2), pp.877–880. Available at: https://doi.org/10.1103/PhysRevA.60.877 [visited on 24 November 2020].

Cabello, A., 1999b. Quantum correlations are not local elements of reality. Physical Review A [Online], 59(1), pp.113–115. Available at: https://doi.org/10.1103/PhysRevA.59.113 [visited on 24 November 2020].

Cańas, G. et al., 2014. Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem. Physical Review A [Online], 90(1), p.012119. Available at: https://doi.org/10.1103/PhysRevA.90.012119 [visited on 24 November 2020].

Cavalcanti, E.G., 2018. Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning. Physical Review X [Online], 8(2), p.021018. Available at: https://doi.org/10.1103/PhysRevX.8.021018 [visited on 24 November 2020].

Charlton, W., 1992. Appendix: Did Aristotle believe in prime matter? In: Aristotle. Physics. Books I and II, Clarendon Aristotle series. Transl. with introd., commentary, note on recent work, and rev. bibliogr. by William Charlton. Oxford: Clarendon Press, 1992, pp.129–145.

Chaves, R. and Fritz, T., 2012. Entropic approach to local realism and noncontextuality. Physical Review A [Online], 85(3), p.032113. Available at: https://doi.org/10.1103/PhysRevA.85.032113 [visited on 24 November 2020].

D’Ariano, G.M. and Yuen, H.P., 1996. Impossibility of measuring the wave function of a single quantum system. Physical Review Letters [Online], 76(16), pp.2832–2835. Available at: https://doi.org/10.1103/PhysRevLett.76.2832 [visited on 24 November 2020].

D’Ambrosio, V. et al., 2013. Experimental implementation of a Kochen-Specker set of quantum tests. Physical Review X [Online], 3(1), p.011012. Available at: https://doi.org/10.1103/PhysRevX.3.011012 [visited on 24 November 2020].

Dhar, H.S. et al., 2017. Monogamy of quantum correlations - a review. In: F.F. Fanchini, S. Pinto, D. de Oliveira and G. Adesso, eds. Lectures on General Quantum Correlations and their Applications [Online], Quantum Science and Technology. Berlin – New York: Springer International Publishing, pp.23–64. Available at: https://doi.org/10.1007/978-3-319-53412-1_3 [visited on 24 November 2020].

Dogra, S., Dorai, K. and Arvind, 2016. Experimental demonstration of quantum contextuality on an NMR qutrit. Physics Letters A [Online], 380(22), pp.1941–1946. Available at: https://doi.org/10.1016/j.physleta.2016.04.015 [visited on 24 November 2020].

Döring, A., 2005. Kochen–Specker theorem for von Neumann algebras. International Journal of Theoretical Physics [Online], 44(2), pp.139–160. Available at: https://doi.org/10.1007/s10773-005-1490-6 [visited on 24 November 2020].

Dummett, M., 1975. Wang’s paradox. Synthese [Online], 30(3), pp.301–324. Available at: https://doi.org/10.1007/BF00485048 [visited on 24 November 2020].

Dürr, D., Goldstein, S. and Zanghě, N., 2013. Quantum Physics without Quantum Philosophy [Online]. Berlin – Heidelberg: Springer-Verlag. Available at: https://doi.org/10.1007/978-3-642-30690-7 [visited on 24 November 2020].

French, S., 2014. The Structure of the World: Metaphysics and Representation. Oxford: Oxford University Press.

Gisin, N., 1998. Quantum cloning without signaling. Physics Letters A [Online], 242(1), pp.1–3. Available at: https://doi.org/10.1016/S0375-9601(98)00170-4 [visited on 24 November 2020].

Gleason, A.M., 1957. Measures on the closed subspaces of a Hilbert space. Journal of Mathematics and Mechanics [Online], 6(6), pp.885–893. Available at: <https://www.jstor.org/stable/24900629> [visited on 25 November 2020].

Hawley, K., 2006. Science as a guide to metaphysics? Synthese [Online], 149(3), pp.451–470. Available at: https://doi.org/10.1007/s11229-005-0569-1 [visited on 25 November 2020].

Hermens, R., 2011. The problem of contextuality and the impossibility of experimental metaphysics thereof. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics [Online], 42(4), pp.214–225. Available at: https://doi.org/10.1016/j.shpsb.2011.06.001 [visited on 25 November 2020].

Heunen, C., Landsman, N.P. and Spitters, B., 2012. Bohrification of operator algebras and quantum logic. Synthese [Online], 186(3), pp.719–752. Available at: https://doi.org/10.1007/s11229-011-9918-4 [visited on 25 November 2020].

Horodecki, K. et al., 2015. Axiomatic approach to contextuality and nonlocality. Physical Review A [Online], 92(3), p.032104. Available at: https://doi.org/10.1103/PhysRevA.92.032104 [visited on 25 November 2020].

Howard, M., Wallman, J., Veitch, V. and Emerson, J., 2014. Contextuality supplies the ‘magic’ for quantum computation. Nature [Online], 510(7505), pp.351–355. Available at: https://doi.org/10.1038/nature13460 [visited on 25 November 2020].

Huang, Y.-F. et al., 2013. Experimental test of state-independent quantum contextuality of an indivisible quantum system. Physical Review A [Online], 87(5), p.052133. Available at: https://doi.org/10.1103/PhysRevA.87.052133 [visited on 25 November 2020].

Jia, Z.-A. et al., 2018. Entropic no-disturbance as a physical principle. Physical Review A [Online], 97(5), p.052128. Available at: https://doi.org/10.1103/PhysRevA.97.052128 [visited on 25 November 2020].

Kirchmair, G. et al., 2009. State-independent experimental test of quantum contextuality. Nature [Online], 460(7254), pp.494–497. Available at: https://doi.org/10.1038/nature08172 [visited on 25 November 2020].

Knoebel, A., 2012. Sheaves of Algebras over Boolean Spaces. New York: Birkhäuser.

Kochen, S. and Specker, E.P., 1967. The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics [Online], 17(1), pp.59–87. Available at: <https://www.jstor.org/stable/24902153> [visited on 25 November 2020].

Konig, R., Renner, R. and Schaffner, C., 2009. The operational meaning of min- and max-entropy. IEEE Transactions on Information Theory [Online], 55(9), pp.4337–4347. Available at: https://doi.org/10.1109/TIT.2009.2025545.

Kurzyński, P., Ramanathan, R. and Kaszlikowski, D., 2012. Entropic test of quantum contextuality. Physical Review Letters [Online], 109(2), p.020404. Available at: https://doi.org/10.1103/PhysRevLett.109.020404 [visited on 25 November 2020].

Lapkiewicz, R. et al., 2011. Experimental non-classicality of an indivisible quantum system. Nature [Online], 474(7352), pp.490–493. Available at: https://doi.org/10.1038/nature10119 [visited on 25 November 2020].

Leibniz, G.W., 2009. Sämtliche Schriften und Briefe. Zweite Reihe, Band 2: Philosophischer Briefwechsel, 1686-1694 [Online]. Berlin: Akademie Verlag. Available at: https://doi.org/10.26015/ADWDOCS-142 [visited on 25 November 2020].

Leifer, M.S., 2014. Ψ-epistemic models are exponentially bad at explaining the distinguishability of quantum states. Physical Review Letters [Online], 112(16), p.160404. Available at: https://doi.org/10.1103/PhysRevLett.112.160404 [visited on 25 November 2020].

Lenzen, W., 1984. Leibniz und die Boolesche Algebra. Studia Leibnitiana [Online], 16(2), pp.187–203. Available at: <https://www.jstor.org/stable/40694003> [visited on 25 November 2020].

Leupold, F.M. et al., 2018. Sustained state-independent quantum contextual correlations from a single ion. Physical Review Letters [Online], 120(18), p.180401. Available at: https://doi.org/10.1103/PhysRevLett.120.180401 [visited on 25 November 2020].

Lewis, D.K., 1986. On the Plurality of Worlds. Oxford: Basil Blackwell.

Liao, K.-Y. et al., 2016. Experimental test of the no-go theorem for continuous ψ-epistemic models. Scientific Reports [Online], 6(1), p.26519. Available at: https://doi.org/10.1038/srep26519 [visited on 25 November 2020].

Liu, B.H. et al., 2009. Experimental demonstration of quantum contextuality with nonentangled photons. Physical Review A [Online], 80(4), p.044101. Available at: https://doi.org/10.1103/PhysRevA.80.044101 [visited on 25 November 2020].

Lostaglio, M. and Senno, G., 2020. Contextual advantage for state-dependent cloning. Quantum [Online], 4, p.258. Available at: https://doi.org/10.22331/q-2020-04-27-258 [visited on 25 November 2020].

Mac Lane, S. and Moerdijk, I., 1992. Sheaves in Geometry and Logic: A First Introduction to Topos Theory, Universitext. New York: Springer-Verlag.

Malink, M. and Vasudevan, A., 2016. The logic of Leibniz’s Generales inquisitiones de analysi notionum et veritatum. The Review of Symbolic Logic [Online], 9(4), pp.686–751. Available at: https://doi.org/10.1017/S1755020316000137 [visited on 25 November 2020].

Marques, B. et al., 2014. Experimental observation of Hardy-like quantum contextuality. Physical Review Letters [Online], 113(25), p.250403. Available at: https://doi.org/10.1103/PhysRevLett.113.250403 [visited on 25 November 2020].

Masanes, L., Acin, A. and Gisin, N., 2006. General properties of nonsignaling theories. Physical Review A [Online], 73(1), p.012112. Available at: https://doi.org/10.1103/PhysRevA.73.012112 [visited on 25 November 2020].

Morreau, M., 2002. What vague objects are like. The Journal of Philosophy [Online], 99(7), pp.333–361. Available at: https://doi.org/10.2307/3655512 [visited on 25 November 2020].

von Neumann, J., 1962. Quantum logics. (Strict- and probability-logics). In: A.H. Taub, ed. Collected Works. Vol. 4: Continuous Geometry and Other Topics. Oxford: Pergamon Press, pp.195–197.

Pati, A.K. and Braunstein, S.L., 2003. Quantum deleting and signalling. Physics Letters A [Online], 315(3), pp.208–212. Available at: https://doi.org/10.1016/S0375-9601(03)01047-8 [visited on 25 November 2020].

Pati, A.K., 2000. Probabilistic exact cloning and probabilistic no-signalling. Physics Letters A [Online], 270(3), pp.103–107. Available at: https://doi.org/10.1016/S0375-9601(00)00281-4 [visited on 25 November 2020].

Pauli, W., 1994. Probability and physics. In: C.P. Enz and K. von Meyenn, eds. Writings on physics and philosophy (R. Schlapp, Trans.). Berlin: Springer, pp.43–48.

Popper, K.R., 1967. Quantum mechanics without ‘the observer’. In: M.A. Bunge, ed. Quantum Theory and Reality, Studies in the Foundations, Methodology and Philosophy of Science 2. Berlin: Springer-Verlag, pp.7–43.

Qu, D. et al., 2020. Experimental entropic test of state-independent contextuality via single photons. Physical Review A [Online], 101(6), p.060101. Available at: https://doi.org/10.1103/PhysRevA.101.060101 [visited on 25 November 2020].

Raussendorf, R., 2013. Contextuality in measurement-based quantum computation. Physical Review A [Online], 88(2), p.022322. Available at: https://doi.org/10.1103/PhysRevA.88.022322 [visited on 25 November 2020].

Ringbauer, M. et al., 2015. Measurements on the reality of the wavefunction. Nature Physics [Online], 11(3), pp.249–254. Available at: https://doi.org/10.1038/nphys3233 [visited on 25 November 2020].

de Ronde, C., 2017. Unscrambling the omelette of quantum contextuality (part 1): Preexistent properties or measurement outcomes? arXiv:1606.03967 [physics, physics:quant-ph] [Online]. Available at: <http://arxiv.org/abs/1606.03967> [visited on 24 November 2020].

Schmid, D. and Spekkens, R.W., 2018. Contextual advantage for state discrimination. Physical Review X [Online], 8(1), p.011015. Available at: https://doi.org/10.1103/PhysRevX.8.011015 [visited on 25 November 2020].

Schrödinger, E., 1935. Science and the Human Temperament. London: G. Allen & Unwin Limited.

Singh, D., Singh, J., Dorai, K. and Arvind, 2019. Experimental demonstration of fully contextual quantum correlations on an NMR quantum information processor. Physical Review A [Online], 100(2), p.022109. Available at: https://doi.org/10.1103/PhysRevA.100.022109 [visited on 25 November 2020].

Specker, E., 1960. Die Logik nicht gleichzeitig entscheidbarer Aussagen. Dialectica [Online], 14(2-3), pp.239–246. Available at: https://doi.org/https://doi.org/10.1111/j.1746-8361.1960.tb00422.x [visited on 25 November 2020].

de Spinoza, B., 1977. Die Ethik: Lateinisch und Deutsch. Revised transl. by Stern, J., Reclams Universal-Bibliothek Nr. 851. Stuttgart: Reclam.

Valentini, A., 2010. De Broglie–Bohm pilot-wave theory: Many worlds in denial? In: S. Saunders, J. Barrett, A. Kent and D. Wallace, eds. Many Worlds?: Everett, Quantum Theory, and Reality [Online]. Oxford: Oxford University Press, pp.476–509. Available at: https://doi.org/10.1093/acprof:oso/9780199560561.003.0019 [visited on 25 November 2020].

Wood, C.J. and Spekkens, R.W., 2015. The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning. New Journal of Physics [Online], 17(3), p.033002. Available at: https://doi.org/10.1088/1367-2630/17/3/033002 [visited on 25 November 2020].

Xiao, Y. et al., 2018. Experimental observation of quantum state-independent contextuality under no-signaling conditions. Optics Express [Online], 26(1), pp.32–50. Available at: https://doi.org/10.1364/OE.26.000032 [visited on 25 November 2020].

Zhang, X. et al., 2013. State-independent experimental test of quantum contextuality with a single trapped ion. Physical Review Letters [Online], 110(7), p.070401. Available at: https://doi.org/10.1103/PhysRevLett.110.070401 [visited on 25 November 2020].

Zu, C. et al., 2012. State-independent experimental test of quantum contextuality in an indivisible system. Physical Review Letters [Online], 109(15), p.150401. Available at: https://doi.org/10.1103/PhysRevLett.109.150401 [visited on 25 November 2020].