The photodetection process under the conditions of an imperfect measurement device

  • George P. Miroshnichenko
  • Alexander Trifanov
Regular Article


The process of cavity mode quantum state photodetection subject to a nonideal measurement device is under consideration. A set of nonorthogonal probabilistic operator valued measures (POVM’s) describing the photodetection process is suggested. The superoperators of conditional system evolution and their Kraus representations are obtained. Developed formalism is used to the quantum state reconstruction problem. We recalculate the probabilities of hypotheses about the initial state of cavity quantum mode in the case of unknown superposition of vacuum and single photon states.


Quantum Information 


  1. 1.
    K. Kraus, States, Effects and Operations. Fundamental notions of quantum theory (Springer-Verlag, Berlin, Heldeiberg, 1983)Google Scholar
  2. 2.
    A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, New York, 2002)Google Scholar
  3. 3.
    Z. Hradil, Phys. Rev. A 55, 1561 (1997)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Y.S. Teo, H. Zhu, B.-G. Englert, J. Rehacek, Z. Hradil, Phys. Rev. Lett. 107, 020404 (2011)ADSCrossRefGoogle Scholar
  5. 5.
    J.F. Poyatos, J.I. Cirac, Phys. Rev. Lett. 78, 390 (1997)ADSCrossRefGoogle Scholar
  6. 6.
    M. Lobino, D. Korystov, C. Kupchak, E. Figueroa, B.C. Sanders, A.I. Lvovsky, Nature 322, 563 (2008)MathSciNetzbMATHGoogle Scholar
  7. 7.
    T. Amri, arXiv:1001.3032v2 [quant-ph]Google Scholar
  8. 8.
    D.P. DiVincenzo, Fortschr. Phys. 48, 771 (2000)zbMATHCrossRefGoogle Scholar
  9. 9.
    C.A. Perez-Delgado, P. Kok, Phys. Rev. Lett. 83, 012303 (2011)ADSGoogle Scholar
  10. 10.
    J.L. O’Brien, A. Furusawa, J. Vuc’kovic’, Nat. Photon. 3, 687 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    L. Mandel, Proc. Phys. Soc. 72, 1037 (1958)ADSCrossRefGoogle Scholar
  12. 12.
    L. Mandel, Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1963), Vol. 2Google Scholar
  13. 13.
    P.L. Kelley, W.H. Kleiner, Phys. Rev. A 136, 316 (1964)MathSciNetADSGoogle Scholar
  14. 14.
    M.D. Srinivas, E.B. Davies, Opt. Act. 28, 981 (1981)MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    H. Carmichael, An open system approach to quantum optics (Springer-Verlag, Berlin, 1993)Google Scholar
  16. 16.
    C.W. Gardiner, Quantum noise (Springer-Verlag, Berlin, 1991)Google Scholar
  17. 17.
    B.R. Mollow, Phys. Rev. 168, 1896 (1968)ADSCrossRefGoogle Scholar
  18. 18.
    P. Zoller, M. Marte, D.F. Walls, Phys. Rev. A 35, 198 (1987)ADSCrossRefGoogle Scholar
  19. 19.
    M. Ueda, N. Imoto, T. Ogawa, Phys. Rev. A 41, 4127 (1990)MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    A.V. Dodonov, S.S. Mizrahi, V.V. Dodonov, J. Opt. B: Quantum. Semiclass. Opt. 7, 99 (2005)ADSCrossRefGoogle Scholar
  21. 21.
    A.V. Dodonov, S.S. Mizrahi, V.V. Dodonov, Phys. Rev. A 72, 023816 (2005)ADSCrossRefGoogle Scholar
  22. 22.
    A.V. Dodonov, S.S. Mizrahi, V.V. Dodonov, Phys. Rev. A 74, 033823 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    D.F. Walls, G.J. Milburn, Quantum optics (Springer-Verlag, New York, 1995)Google Scholar
  24. 24.
    L. Mandel, E. Wolf, Optical coherence and quantum optics (Cambridge University Press, Cambridge, 1995)Google Scholar
  25. 25.
    M.C. Oliveira, S.S. Mizrahi, V.V. Dodonov, J. Opt. B: Quantum Semiclass. Opt. 5, S271 (2003)CrossRefGoogle Scholar
  26. 26.
    A.V. Dodonov, S.S. Mizrahi, V.V. Dodonov, Phys. Rev. A 75, 013806 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    C. Wagner, R.J. Brecha, A. Schenzle, H. Walther, Phys. Rev. A 47, 5068 (1993)ADSCrossRefGoogle Scholar
  28. 28.
    H.-J. Briegel, B.-G. Englert, N. Sterpi, H. Walther, Phys. Rev. A 49, 2962 (1994)ADSCrossRefGoogle Scholar
  29. 29.
    G.P. Miroshnichenko, Zh. Eksp. Theor. Fiz. 131, 829 (2007)Google Scholar
  30. 30.
    G.P. Miroshnichenko, Zh. Eksp. Theor. Fiz. 139, 1055 (2011)Google Scholar
  31. 31.
    H. Terashima, Phys. Rev. A 83, 032111 (2011)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Saint-Petersburg National Research University of Information TechnologiesSaint PetersburgRussia

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