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.
References
[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.
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. http://dx.doi.org/10.1023/A:1026096313729
[8]
Groblacher,
S., Paterek, T., Kaltenbaek, R., Brukner, C., Zukowski, M., Aspelmeyer, M. and
Zeilinger, A. (2007) An Experimental
Test of Non-Local Realism. Nature (London), 446, 871-875. http://dx.doi.org/10.1038/nature05677
[9]
Paterek, T., Fedrizzi, A., Groblacher, S., Jennewein, T., Zukowski, 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. http://dx.doi.org/10.1103/PhysRevLett.99.210406
[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. http://dx.doi.org/10.1103/PhysRevLett.99.210407
[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. http://dx.doi.org/10.1098/rspa.1985.0070
[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. http://dx.doi.org/10.1063/1.476739
[13]
Gulde,
S., Riebe, M., Lancaster, G.P.T., Becher, C., Eschner, J., Haffner, 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. http://dx.doi.org/10.1038/nature01336
[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. http://dx.doi.org/10.1088/1464-4266/7/9/009
[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. http://dx.doi.org/10.1103/PhysRevLett.91.187903
[17]
Tame,
M.S., Prevedel, R., Paternostro, M., Bohi, 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. http://dx.doi.org/10.1103/PhysRevLett.98.140501
[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. http://dx.doi.org/10.1103/PhysRevA.64.023806
[19]
Nagata,
K. (2010) Implementation
of the Deutsch-Jozsa Algorithm Violates Nonlocal Realism. The European Physical Journal D, 56, 441-444. http://dx.doi.org/10.1140/epjd/e2009-00303-6
