Skip to main content
SpringerLink
Log in

Two-time correlations functions and quantumness of an open two-level system

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

Joint probability of obtaining outcomes in projective measurement performed sequentially on a two-level system at two different times is derived to investigate quantumness of the system, where the two-level system is influenced by a thermal reservoir with finite correlation time. Two-time correlation functions of the Pauli operators are also obtained. The joint probability and the two-time correlation functions are calculated by making use of the formulas developed recently by Ban et al. [Phys. Rev. A 97, 052101 (2018)] since the quantum regression theorem cannot be applied due to the finiteness of the reservoir correlation time. It is shown that the finiteness of the reservoir correlation time enhances the quantum witnesses of the two-level system. Furthermore the violation of the Leggett–Garg inequality is examined.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987)

  2. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, S. Wehner, Rev. Mod. Phys. 86, 419 (2014)

    Article  ADS  Google Scholar 

  3. A. Einstein, B. Podolski, N. Rosen, Phys.  Rev. 47, 777 (1935)

    Article  ADS  Google Scholar 

  4. M.A. Nielsen, I.L. Chuang, Quantum Communication and Quantum Information (Cambridge University Press, Cambridge, 1987)

  5. J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  Google Scholar 

  6. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, Rev. Mod. Phys. 86, 021002 (2014)

    Google Scholar 

  7. H. Wiseman, S.J. Jones, A. Doherty, Phys. Rev. Lett. 98, 140402 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  8. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  Google Scholar 

  9. A.J. Leggett, A. Garg, Phys. Rev. Lett. 54, 857 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  10. A.J. Leggett, Rep. Prog. Phys. 71, 022001 (2008)

    Article  ADS  Google Scholar 

  11. C. Emary, N. Lambert, F. Nori, Rep.  Prog.  Phys. 77, 016001 (2014)

    Article  ADS  Google Scholar 

  12. M.E. Goggin, M.P. Almeida, M. Barbieri, B.P. Lanyon, J.L. O’brien, A.G. White, G.J. Pryde, Proc. Natl. Acad. Sci. 108, 1256 (2011)

    Article  ADS  Google Scholar 

  13. A. Palacios-Laloy, F. Mallet, F. Nguyen, P. Berlet, D. Vion, D. Esteve, A. Korotkov, Nat. Phys. 6, 442 (2010)

    Article  Google Scholar 

  14. T.M. Cover, J.A. Thomas, Elements of Information Theory (Wiley, New York, 1991)

  15. C.M. Li, N. Lambert, Y.N. Chen, G.Y. Chen, F. Nori, Sci. Rep. 2, 885 (2012)

    Article  Google Scholar 

  16. G. Schild, C. Emary, Phys. Rev. A 92, 032101 (2015)

    Article  ADS  Google Scholar 

  17. R. Alicki, N.V. Ryn, J. Phys. A 41, 062001 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  18. R. Alicki, M. Piani, N.V. Ryn, J. Phys. A 41, 495303 (2008)

    Article  MathSciNet  Google Scholar 

  19. P. Facchi, S. Pascazio, V. Vedral, K. Yuasa, J. Phys. A 45, 105302 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  20. R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II (Springer, Berlin, 1991)

  21. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1993)

  22. H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2006)

  23. A. Rivas, S.F. Huelga, M.B. Plenio, Rep. Prog. Phys. 77, 094001 (2014)

    Article  ADS  Google Scholar 

  24. H.P. Breuer, E. Laine, J. Piilo, B. Vacchini, Rev.  Mod. Phys. 88, 021002 (2016)

    Article  ADS  Google Scholar 

  25. I. de Vega, D. Alonso, Rev. Mod. Phys. 89, 015001 (2017)

    Article  ADS  Google Scholar 

  26. H. Goan, P. Chen, C. Jian, J. Chem. Phys. 134, 124112 (2011)

    Article  ADS  Google Scholar 

  27. G. Guarnieri, A. Smirne, B. Vacchini, Phys. Rev. A 90, 022110 (2014)

    Article  ADS  Google Scholar 

  28. M. Ban, S. Kitajima, F. Shibata, Phys. Rev. A 97, 052101 (2018)

    Article  ADS  Google Scholar 

  29. A. Friedenberger, E. Lutz, Phys. Rev. A 95, 022101 (2017)

    Article  ADS  Google Scholar 

  30. M. Ban, S. Kitajima, F. Shibata, J.  Phys. A 38,  7161 (2005)

    Article  ADS  Google Scholar 

  31. T. Fritz, New J. Phys. 12, 083055 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo, 112-8610, Japan

    Masashi Ban

Authors
  1. Masashi Ban
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Masashi Ban.

Additional information

Contribution to the Topical Issue “Quantum Correlations”, edited by Marco Genovese, Vahid Karimipour, Sergei Kulik, and Olivier Pfister.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ban, M. Two-time correlations functions and quantumness of an open two-level system. Eur. Phys. J. D 73, 12 (2019). https://doi.org/10.1140/epjd/e2018-90399-8

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2018-90399-8

Search

Navigation