Weak Values Influenced by Environment

DOI: 10.4236/jmp.2013.411A1001   PDF   HTML   XML   3,439 Downloads   4,947 Views   Citations


A weak value of an observable is studied for a quantum system which is placed under the influence of an environment, where a quantum system irreversibly evolves from a pre-selected state to a post-selected state. A general expression for a weak value influenced by an environment is provided. For a Markovian environment, the weak value is calculated in terms of the predictive and retrodictive density matrices, or by means of the quantum regression theorem. For a non-Markovian environment, a weak value is examined by making use of exactly solvable models. It is found that although the anomalous property is significantly suppressed by a Markovian environment, it can survive a non-Markovian environment.

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M. Ban, "Weak Values Influenced by Environment," Journal of Modern Physics, Vol. 4 No. 11A, 2013, pp. 1-8. doi: 10.4236/jmp.2013.411A1001.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. Von Neumann, “Mathematical Foundations of Quantum Mechanics,” Princeton University Press, New Jersey, 1955.
[2] Y. Aharonov, D. Z. Albert and L. Vaidman, Physical Review Letters, Vol. 60, 1988, pp. 1351-1354.
[3] I. M. Duck, Physical Review D, Vol. 40, 1989, pp. 2112-2117. http://dx.doi.org/10.1103/PhysRevD.40.2112
[4] Y. Aharonov and L. Vaidman, Physical Review A, Vol. 41, 1990, pp. 11-20.
[5] H. M. Wiseman, Physical Review A, Vol. 65, 2002, Article ID: 032111.
[6] L. M. Johansen, Physical Review Letters, Vol. 93, 2004, Article ID: 120402.
[7] L. M. Johansen and A. Luis, Physical Review A, Vol. 70, 2004, Article ID: 052115.
[8] L. M. Johansen, Physical Letters A, Vol. 322, 2004, pp. 298-300. http://dx.doi.org/10.1016/j.physleta.2004.01.041
[9] R. Jozsa, Physical Review A, Vol. 76, 2007, Article ID: 044103. http://dx.doi.org/10.1103/PhysRevA.76.044103
[10] A. C. Lobo, Physical Review A, Vol. 80, 2009, Article ID: 012112. http://dx.doi.org/10.1103/PhysRevA.80.012112
[11] T. Geszti, Physical Review A, Vol. 81, 2010, Article ID: 044102. http://dx.doi.org/10.1103/PhysRevA.81.044102
[12] X. Zhu, Y. Zhang, S. Pang, C. Qiao, Q. Liu and S. Wu, Physical Review A, Vol. 84, 2011, Article ID: 052111.
[13] S. Wu and Y. Li, Physical Review A, Vol. 83, 2011, Article ID: 052106.
[14] A. G. Kofman, S. Ashhab and F. Nori, Physics Report, Vol. 520, 2012, pp. 43-133.
[15] P. B. Dixon, D. J. Starling, A. N. Jordan and J. C. Howell, Physical Review Letters, Vol. 102, 2009, Article ID: 173601.
[16] D. J. Starling, P. B. Dixon, A. N. Jordan and J. C. Howell, Physical Review A, Vol. 82, 2010, Article ID: 063822.
[17] R. Kubo, M. Toda and N. Hashitsume, “Statistical Physics II,” Springer, Berlin, 1985.
[18] H. Breuer and F. Petruccione, “The Theory of Open Quantum System,” Oxford University Press, Oxford, 2006.
[19] M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” Cambridge University Press, Cambridge, 2000.
[20] R. Alicki and K. Lendi, “Quantum Dynamical Semigroups and Applications,” Springer, Berlin, 2007.
[21] S. M. Barnett, D. T. Pegg, J. Jeffers and O. Jedrkiewicz, Physical Review Letters, Vol. 86, 2001, pp. 2455-2458.
[22] P. W. Anderson, Journal of the Physical Society of Japan, Vol. 9, 1954, pp. 316-339.
[23] R. Anderson, Journal of the Physical Society of Japan, Vol. 9, 1954, pp. 935-944.
[24] M. Ban, S. Kitajima and F. Shibata, Physics Letters A, Vol. 349, 2006, pp. 415-421.
[25] N. G. van Kampen, “Stochastic Processes in Physics and Chemistry,” Elsevier, Amsterdam, 1981.
[26] M. Ban, S. Kitajima and F. Shibata, Physics Letters A, Vol. 375, 2011, pp. 2283-2290.

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