International Journal of Theoretical Physics

, Volume 54, Issue 12, pp 4356–4366 | Cite as

Getting Information via a Quantum Measurement: The Role of Decoherence

  • Pietro Liuzzo-Scorpo
  • Alessandro Cuccoli
  • Paola VerrucchiEmail author


In this work we investigate the relation between quantum measurements and decoherence, in order to formally express the necessity of the latter for obtaining an informative output from the former. To this aim, we analyse the dynamical behaviour of a particular model, which is often adopted in the literature for describing projector valued measures of discrete observables. The analysis is developed by a recently introduced method for studying open quantum systems, namely the parametric representation with environmental coherent states: this method allows us to determine a necessary condition that the evolved quantum state of the apparatus must fulfil in order to have the properties that a measurement scheme requests it to feature. We find that this condition strictly implies decoherence in the system object of the measurement, with respect to the eigenstates of the hermitian operator that represents the measured observable. The relevance of dynamical entanglement generation is highlighted, and consequences of the possible macroscopic structure of the measurement apparatus are also commented upon.


Open quantum systems Decoherence Quantum measurement 



This work has been done in the framework of the Convenzione operativa between the Institute for Complex Systems of the italian National Research Council, and the Physics and Astronomy Department of the Univeristy of Florence.


  1. 1.
    Busch, P., Lathi, J.P., Mittelstaedt, P.: The quantum theory of measurement. Springer, Berlin (1996)zbMATHGoogle Scholar
  2. 2.
    Namiki, M., Pascazio, S., Nakazato, H.: Decoherence and Quantum Measurements. World Scientific (1997)Google Scholar
  3. 3.
    Zurek, W.H.: Rev. Mod. Phys. 75, 715 (2003)Google Scholar
  4. 4.
    Schlosshauer, M.: Decoherence and the Quantum-To-Classical Transition. The Frontiers Collection. Springer (2007)Google Scholar
  5. 5.
    Ghirardi, G., Rimini, A., Weber, T.: In: Accardi, L. et al. (eds.) Quantum Probability and Applications (1985)Google Scholar
  6. 6.
    Ghirardi, G., Rimini, A., Weber, T.: Phys. Rev. D 34, 470 (1986)MathSciNetCrossRefADSzbMATHGoogle Scholar
  7. 7.
    Nakazato, H., Pascazio, S.: Phys. Rev. A 48, 1066 (1993)CrossRefADSGoogle Scholar
  8. 8.
    Mermin, D.: Am. J. Phys. 66, 753 (1998)CrossRefADSGoogle Scholar
  9. 9.
    Kraus, K.: States, Effects, and Operations. Springer, Berlin (1983)zbMATHGoogle Scholar
  10. 10.
    Breuer, H.P., Petruccione, F.: The theory of open quantum systems. Oxford University Press (2002)Google Scholar
  11. 11.
    Holevo, A.S.: Quantum systems, channels, information: a mathematical introduction, vol. 16. Walter de Gruyter (2012)Google Scholar
  12. 12.
    Rivas, A., Huelga, S.F.: Open Quantum Systems: An Introduction. Springer, Berlin (2012)CrossRefGoogle Scholar
  13. 13.
    Calvani, D., Cuccoli, A., Gidopoulos, N.I., Verrucchi, P.: Proceedings of the National Academy of Sciences 110(17), 6748 (2013)Google Scholar
  14. 14.
    D’Ariano, G.M., Lo Presti, P.: Phys. Rev. Lett. 86, 4195 (2001)CrossRefADSGoogle Scholar
  15. 15.
    D’Ariano, G.M., Maccone, L., Paris, M.G.A.: Phys. Lett. A 276, 25 (2000)MathSciNetCrossRefADSzbMATHGoogle Scholar
  16. 16.
    von Neumann, J. Mathematical Foundations of Quantum Mechanics. Princeton University Press (1996). Translation from GermanGoogle Scholar
  17. 17.
    London, F., Bauer, E.: La teorie de l’observation en mecanique quantique (Herman et cie (1939)Google Scholar
  18. 18.
    Wigner, E.: Z. Phys. 133, 101 (1952)MathSciNetCrossRefADSzbMATHGoogle Scholar
  19. 19.
    Araki, H., Yanase, M.M.: Phys. Rev. 120, 622 (1960)MathSciNetCrossRefADSzbMATHGoogle Scholar
  20. 20.
    Yanase, M.M.: Phys. Rev. 123, 666 (1961)CrossRefADSGoogle Scholar
  21. 21.
    Shimony, A., Stein, H.: In: B. D’Espagnat (ed.) Foundations of Quantum Mechanics, pp. 56–76. Academic Press, New York (1971)Google Scholar
  22. 22.
    Shimony, A., Stein, H.: Am. Math. Mon. 86, 292 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Busch, P.: Found. Phys. 17(9), 905 (1987)MathSciNetCrossRefADSGoogle Scholar
  24. 24.
    Busch, P., Schroeck, J.: Found. Phys. 19(7), 807 (1989)MathSciNetCrossRefADSGoogle Scholar
  25. 25.
    Ozawa, M.: J. Math. Phys. 25, 79 (1984)CrossRefGoogle Scholar
  26. 26.
    Calvani, D., Cuccoli, A., Gidopoulos, N.I., Verrucchi, P.: Open Syst. Inform. Dynam. 20(3) (2013)Google Scholar
  27. 27.
    Zhang, W.M., Feng, D.H., Gilmore, R.: Rev. Mod. Phys. 62, 867 (1990)Google Scholar
  28. 28.
    Perelomov, A.: Commun. Math. Phys. 26(3), 222 (1972)MathSciNetCrossRefADSzbMATHGoogle Scholar
  29. 29.
    Comberscure, M., Robert, D.: Coherent States and Application in Mathematical Physics. Springer, Berlin (2012)CrossRefGoogle Scholar
  30. 30.
    Yaffe, L.G.: Rev. Mod. Phys. 54, 407 (1982)MathSciNetCrossRefADSGoogle Scholar
  31. 31.
    Lieb, E.H.: Commun. Math. Phys. 31(4), 327 (1973)MathSciNetCrossRefADSzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Pietro Liuzzo-Scorpo
    • 1
    • 2
  • Alessandro Cuccoli
    • 1
  • Paola Verrucchi
    • 3
    Email author
  1. 1.Dipartimento di Fisica Università di Firenze, and INFN Sezione di FirenzeSesto FiorentinoItaly
  2. 2.School of Mathematical SciencesThe University of NottinghamNottinghamUK
  3. 3.Istituto dei Sistemi Complessi ISC-CNR, Dipartimento di Fisica Università di Firenze, and INFN Sezione di FirenzeSesto FiorentinoItaly

Personalised recommendations