Review on investigating the possibility of local hidden variable theories-quantum teleportation

  • Authors

    • Dorcas Attuabea Addo Department of Mathematics, Kwame Nkrumah University of Science and TechnologyKumasi-Ghana
    • Steven Abel Department of Mathematics, Durham University
    • Richard Kwame Ansah Department of Mathematics, Durham University , Durham of Mathematics and Statistics, University of Energy and Natural Resources
    • Isaac Nkrumah Department of Physics, Kwame Nkrumah University of Science and Technology
    2018-01-14
    https://doi.org/10.14419/ijams.v6i1.8755
  • Bell's inequality, Classical Mechanics, Local Hidden Variable, Quantum Teleportation, Superpossition

  • The core of the paper was to investigate the possibility of local hidden variable theory and its application in quantum teleportation. We reviewed literature on the Bell's inequality which is necessary for quantum teleportation. Quantum teleportation utilises a single-particle entangled state which can be successfully achieved by the application of the locality assumption which leads to Bell's inequality. A violation of the Bell's inequality signifies the nonlocal nature of a single particle useful for quantum teleportation.

  • References

    1. [1] Alain Aspect, “Bell’s theorem: the naive view of an experimentalistâ€, Springer, (2002).

      [2] Barrett, M. D., Chiaverini, J., Schaetz, T., & Britton, J., “Deterministic quantum teleportation of atomic qubitsâ€, Nature, Vol.429, No.6993, (2004).

      [3] Bell, J. S., “Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophyâ€, Cambridge university press, (2004).

      [4] Bell, J. S., “On the impossible pilot waveâ€, Foundations of Physics,

      [5] Vol.12, No.10, (1982), pp.989-999

      [6] Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A. and Wootters, W. K., “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channelsâ€, Physical review letters, Vol.70, No.13, (1993), p.1895.

      [7] Blaylock, Guy. “The EPR paradox, Bell’s inequality, and the question of localityâ€, American Journal of Physics, Vol.78, No.1, (2010), p:111-120.

      [8] Dada, A. C., Leach, J., Buller, G. S., Padgett, M. J., & Andersson, E., “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalitiesâ€, Nature Physics, Vol.7, No.9, (2011), 677-680.

      [9] Dirac, P. A. M., “The principles of quantum mechanics â€, Oxford

      [10] university press, No.27, (1981).

      [11] Einstein, A., Podolsky, B. and Rosen, N., “Can quantum-mechanical description of physical reality be considered complete?â€, Physical review, Vol.47, No.10, (1935), p.777.

      [12] Genovese, M., “Research on hidden variable theories: A review of recent progressesâ€, Physics Reports, Vol.413, No.6, (2005), pp.319-396.

      [13] Griffiths, D. J., “Introduction to quantum mechanicsâ€, Pearson Education India.

      [14] Hasegawa, Yuji, Rudolf Loidl, Gerald Badurek, Matthias Baron, and Helmut Rauch, “Violation of a Bell-like inequality in single-neutron nterferometryâ€, Nature 425, No. 6953, (2003), pp:45-48.

      [15] Home, D. and Selleri, F., “Bell’s theorem and the EPR paradoxâ€, LaRivista del Nuovo Cimento, Vol.14, No.9, (1978-1999), pp.1-95.

      [16] Horodecki, R., Horodecki, M. and Horodecki, P., “Teleportation, Bell’s inequalities and inseparabilityâ€, Physics Letters A, Vol.222, No.1-2, (1996), pp.21-25.

      [17] Hu, M. L., “Teleportation of the one-qubit state in decoherence environmentsâ€, Journal of Physics B: Atomic, Molecular and Optical Physics, Vol.44, No.2, (2011), p.025502.

      [18] J. S. Bell et al., “On the einstein-podolsky-rosen paradoxâ€, Physics, Vol.1, No.3, (1964), pp:195-200.

      [19] Klöck, D., “Quantum Computersâ€.Lee, J. and Kim, M. S., “Entanglement teleportation via Werner statesâ€, Physical review letters, Vol.84, No.18, (2000), p.4236.

      [20] R. Horodecki, M. Horodecki, and P. Horodecki, “Teleportation, bell’s inequalities and inseparabilityâ€, Physics Letters A, Vol.222, No.1, (1996), pp:21-25.

      [21] Reilly, Michael H. “Temperature dependence of the short wavelength transmittance limit of vacuum ultraviolet window materials—II theoretical, including interpretations for UV spectra of SiO2, GeO2, and Al2O3â€, Journal of Physics and Chemistry of Solids 31, No. 5, (1970), pp: 1041-1056.

      [22] Riebe, M., Haffner, H., Roos, C. F., & Hansel, W., “Deterministic quantum teleportation with atomsâ€, Nature, Vol.429, No.6993, (2002), p.734.

      [23] Shankar, R., “Principles of quantum mechanicsâ€, Springer Science & Business Media, (2012).

      [24] S. Turgut., “Measurement process in quantum mechanicsâ€, Vol.1,(2013).

      [25] Tang, C. L., “Fundamentals of quantum mechanics: for solid state electronics and opticsâ€, Cambridge University Press, (2005).

      [26] Terhal, B. M., Doherty, A. C., & Schwab, D., “Symmetric extensions of quantum states and local hidden variable theoriesâ€, Physical review letters, Vol.90, No.15, (2003).

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  • How to Cite

    Addo, D. A., Abel, S., Ansah, R. K., & Nkrumah, I. (2018). Review on investigating the possibility of local hidden variable theories-quantum teleportation. International Journal of Advanced Mathematical Sciences, 6(1), 1-9. https://doi.org/10.14419/ijams.v6i1.8755