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Quantum Contextuality is in Good Agreement with the Delayed-Choice Method

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Abstract

Contextuality is a critical concept to understand the laws of Quantum Theory. It tells us how measurement can be affected by the context in which it is performed. As a result, we observe the violation of the classical inequalities. The wave-particle duality is also a fundamental concept explaining how quantum particles may behave as both waves and particles. In this work, we make a connection between quantum contextuality and the wave-particle duality. For this purpose, we propose a quantum circuit consisting of a couple of two-qubit gates and a Hadamard gate. We apply the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) test to the symmetric two-qubit states corresponding to qutrits and observe that particle- and wave-like properties determine whether one may observe contextual behavior.

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References

  1. Gleason, A.: Measures on the closed subspaces of a hilbert space. Indiana Univ. Math. J. 6, 885–893 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bell, J.S.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447 (1966)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Specker, E.P.: Die logik nicht gleichzeitig entsc heidbarer aussagen. Dialectica. 14, 239–246 (1960)

    Article  MathSciNet  Google Scholar 

  4. Kochen, S., Specker, E.P.: The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967)

    MathSciNet  MATH  Google Scholar 

  5. Ionicioiu, R., Terno, D.R.: Proposal for a quantum delayed-choice experiment. Phys. Rev. Lett. 107, 230406 (2011)

    Article  ADS  Google Scholar 

  6. Zheng, S.B., Zhong, Y.P., Xu, K., Wang, Q.J., Wang, H., Shen, L.T., Yang, C.P., Martinis, J.M., Cleland, A.N., Han, S.Y.: Quantum delayed-choice experiment with a beam splitter in a quantum superposition. Phys. Rev. Lett. 115, 260403 (2015)

    Article  ADS  Google Scholar 

  7. Liu, K., Xu, Y., Wang, W., Zheng, S.B., Roy, T., Kundu, S., Chand, M., Ranadive, A., Vijay, R., Song, Y., Duan, L., Sun, L.: A twofold quantum delayed-choice experiment in a superconducting circuit. Sci. Adv. 3, 1603159 (2017)

    Article  Google Scholar 

  8. Xin, T., Li, H., Wang, B.X., Long, G.L.: Realization of an entanglement-assisted quantum delayed-choice experiment. Phys. Rev. A. 92, 022126 (2015)

    Article  ADS  Google Scholar 

  9. Chen, X., Deng, Y., Liu, S., et al.: A generalized multipath delayed-choice experiment on a large-scale quantum nanophotonic chip. Nat. Commun. 12, 2712 (2021)

    Article  ADS  Google Scholar 

  10. Tang, J.S., Li, Y.L., Xu, X.Y., Guo, G.C., Li, C.F., Xiang, G.Y.: Realization of quantum wheeler’s delayed-choice experiment. Nature Photon. 6, 600–604 (2012)

    Article  ADS  Google Scholar 

  11. Roy, S.S., Shukla, A., Mahesh, T.S.: Nmr implementation of a quantum delayed-choice experiment. Phys. Rev. A 85, 022109 (2012)

    Article  ADS  Google Scholar 

  12. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  MATH  Google Scholar 

  13. Peruzzo, A., Shadbolt, P., Brunner, N., Popescu, S., O’Brien, J.L.: A quantum delayed-choice experiment. Science 338, 634–637 (2012)

    Article  ADS  Google Scholar 

  14. Gisin, N.: Bell’s inequality holds for all non-product states. Phys. Lett. A. 154, 201–202 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  15. Diker, F.: Mathematical relation between concurrence and intensity of a photon in the quantum delayed-choice experiment. J. Phys.: Conf. Ser. 2148, 012010 (2022)

    Google Scholar 

  16. Gupta, S., Saha, D., Xu, Z.P., Cabello, A., Majumdar, A.S.: Quantum contextuality provides communication complexity advantage. Phys. Rev. Lett. 130, 080802 (2023)

    Article  ADS  MathSciNet  Google Scholar 

  17. Bell, J.S.: On the einstein podolsky rosen paradox. Physics. 1, 195 (1964)

    Article  MathSciNet  Google Scholar 

  18. Aspect, A., Dalibard, J., Roger, G.: Experimental test of bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  19. Freedman, S.J., Clauser, J.F.: Experimental test of local hidden-variable theories. Phys. Rev. Lett. 28, 938 (1972)

    Article  ADS  Google Scholar 

  20. Klyachko, A.: Coherent states, entanglement, and geometric invariant theory. https://arxiv.org/abs/quant-ph/0206012 (2002)

  21. Klyachko, A.: Dynamical symmetry approach to entanglement. In: Gazeau, J.P., Nešetřil, J., Rovan, B. (eds.) Physics and Theoretical Computer Science: from Numbers and Languages to (quantum) Cryptography Security, pp. 25–54. Ios Press, Amsterdam (2007)

    Google Scholar 

  22. Binicioǧlu, S., Can, M.A., Klyachko, A.A., Shumovsky, A.S.: Entanglement of a single spin-1 object: an example of ubiquitous entanglement. Found. Phys. 37, 1253–1277 (2007)

    Article  ADS  MATH  Google Scholar 

  23. Klyachko, A.A., Can, M.A., Binicioğlu, S., Shumovsky, A.S.: Simple test for hidden variables in spin-1 systems. Phys. Rev. Lett. 101, 020403 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Ahrens, J., Amselem, E., Cabello, A., Bourennane, M.: Two fundamental experimental tests of nonclassicality with qutrits. Sci. Rep. 3, 1 (2013)

    Article  Google Scholar 

  25. Łapkiewicz, R., Li, P., Schaeff, C., Langford, N., Ramelow, S., Wiésniak, M., Zeilinger, A.: Experimental non-classicality of an indivisible quantum system. Nature. 474, 490–493 (2011)

    Article  Google Scholar 

  26. Kurzyński, P., Kaszlikowski, D.: Contextuality of almost all qutrit states can be revealed with nine observables. Phys. Rev. A. 86, 042125 (2012)

    Article  ADS  Google Scholar 

  27. Yu, S., Oh, C.H.: State-independent proof of kochen-specker theorem with 13 rays. Phys. Rev. Lett. 108, 030402 (2012)

    Article  ADS  Google Scholar 

  28. Can, M.A., Klyachko, A.A., Shumovsky, A.S.: Single-particle entanglement. J. Opt. B: Quantum Semiclass. Opt. 7, 1 (2005)

    Article  MathSciNet  Google Scholar 

  29. Wootters, W.K., Zurek, W.H.: Complementarity in the double-slit experiment: quantum nonseparability and a quantitative statement of bohr’s principle. Phys. Rev. D. 19, 473 (1979)

    Article  ADS  Google Scholar 

  30. Glauber, R.J.: Amplifiers, attenuators, and schrödinger’s cat a. Ann. N.Y. Acad. Sci. 480, 336–372 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  31. Greenberger, D.M., Yasin, A.: Simultaneous wave and particle knowledge in a neutron interferometer. Phys. Lett. A. 128, 391–394 (1988)

    Article  ADS  Google Scholar 

  32. Durr, S., Rempe, G.: Can wave-particle duality be based on the uncertainty relation? Am. J. Phys. 68, 1021–1024 (2000)

    Article  ADS  Google Scholar 

  33. Englert, B.G.: Fringe visibility and which-way information: an inequality. Phys. Rev. Lett. 77, 2154 (1996)

    Article  ADS  Google Scholar 

  34. Huang, J.H., Zhu, S.Y.: Complementarity and uncertainty in a two-way interferometer. https://arxiv.org/abs/1011.5273 (2010)

  35. Busch, P., Shilladay, C.: Complementarity and uncertainty in mach-zehnder interferometry and beyond. Phys. Rep. 435, 1–31 (2006)

    Article  ADS  Google Scholar 

  36. Diker, F., Gedik, Z.: The degree of quantum contextuality in terms of concurrence for the kcbs scenario. Int. J. Theor. Phys. 61, 266 (2022)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Dr. Firat Diker would like to dedicate this work to the people who have lost their lives and those who have been affected by the earthquake in Turkey and Syria.

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  1. Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, 34956, Istanbul, Turkey

    Fırat Diker

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Diker, F. Quantum Contextuality is in Good Agreement with the Delayed-Choice Method. Int J Theor Phys 62, 116 (2023). https://doi.org/10.1007/s10773-023-05344-6

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