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Can Hidden Variables Theories Meet Quantum Computation?

DOI: 10.4236/oalib.1101804    614 Downloads   885 Views  


We study the relation between hidden variables theories and quantum computation. We discuss an inconsistency between a hidden variables theory and controllability of quantum computation. To derive the inconsistency, we use the maximum value of the square of an expected value. We propose a solution of the problem by using new hidden variables theory. Also we discuss an inconsistency between hidden variables theories and the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be an easy detector to Pauli observable. We cannot accept hidden variables theories to simulate the double-slit experiment in a specific case. Hidden variables theories may not depicture quantum detector. This is a quantum measurement theoretical profound problem.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Nagata, K. and Nakamura, T. (2015) Can Hidden Variables Theories Meet Quantum Computation?. Open Access Library Journal, 2, 1-12. doi: 10.4236/oalib.1101804.


[1] von Neumann, J. (1955) Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton.
[2] Feynman, R.P., Leighton, R.B. and Sands, M. (1965) Lectures on Physics. Volume 3, Quantum Mechanics, Addison-Wesley Publishing Company.
[3] Redhead, M. (1989) Incompleteness, Nonlocality, and Realism. 2nd Edition, Clarendon Press, Oxford.
[4] Peres, A. (1993) Quantum Theory: Concepts and Methods. Kluwer Academic, Dordrecht.
[5] Sakurai, J.J. (1995) Modern Quantum Mechanics. Addison-Wesley Publishing Company.
[6] Nielsen, M.A. and Chuang, I.L. (2000) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge.
[7] Leggett, A.J. (2003) Nonlocal Hidden-Variable Theories and Quantum Mechanics: An Incompatibility Theorem. Foundations of Physics, 33, 1469-1493.
[8] Gröblacher, S., Paterek, T., Kaltenbaek, R., Brukner, Č., Żukowski, M., Aspelmeyer, M. and Zeilinger, A. (2007) An Experimental Test of Non-Local Realism. Nature (London), 446, 871-875.
[9] Paterek, T., Fedrizzi, A., Gröblacher, S., Jennewein, T., Żukowski, M., Aspelmeyer, M. and Zeilinger, A. (2007) Experimental Test of Nonlocal Realistic Theories without the Rotational Symmetry Assumption. Physical Review Letters, 99, Article ID: 210406.
[10] Branciard, C., Ling, A., Gisin, N., Kurtsiefer, C., Lamas-Linares, A. and Scarani, V. (2007) Experimental Falsification of Leggett’s Nonlocal Variable Model. Physical Review Letters, 99, Article ID: 210407.
[11] Deutsch, D. (1985) Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer. Proceedings of the Royal Society of London. Series A, 400, 97.
[12] Jones, J.A. and Mosca, M. (1998) Implementation of a Quantum Algorithm on a Nuclear Magnetic Resonance Quantum Computer. The Journal of Chemical Physics, 109, 1648.
[13] Gulde, S., Riebe, M., Lancaster, G.P.T., Becher, C., Eschner, J., Häffner, H., Schmidt-Kaler, F., Chuang, I.L. and Blatt, R. (2003) Implementation of the Deutsch-Jozsa Algorithm on an Ion-Trap Quantum Computer. Nature, 421, 48-50.
[14] de Oliveira, A.N., Walborn, S.P. and Monken, C.H. (2005) Implementing the Deutsch Algorithm with Polarization and Transverse Spatial Modes. Journal of Optics B: Quantum and Semiclassical Optics, 7, 288-292.
[15] Kim, Y.-H. (2003) Single-Photon Two-Qubit Entangled States: Preparation and Measurement. Physical Review A, 67, Article ID: 040301(R).
[16] Mohseni, M., Lundeen, J.S., Resch, K.J. and Steinberg, A.M. (2003) Experimental Application of Decoherence-Free Subspaces in an Optical Quantum-Computing Algorithm. Physical Review Letters, 91, Article ID: 187903.
[17] Tame, M.S., Prevedel, R., Paternostro, M., Böhi, P., Kim, M.S. and Zeilinger, A. (2007) Experimental Realization of Deutsch’s Algorithm in a One-Way Quantum Computer. Physical Review Letters, 98, Article ID: 140501.
[18] Schon, C. and Beige, A. (2001) Analysis of a Two-Atom Double-Slit Experiment Based on Environment-Induced Measurements. Physical Review A, 64, Article ID: 023806.
[19] Nagata, K. (2010) Implementation of the Deutsch-Jozsa Algorithm Violates Nonlocal Realism. The European Physical Journal D, 56, 441-444.

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