Skip to main content
SpringerLink
Log in

Generalized measures of quantum correlations for mixed states

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

The exponential speedup achieved in certain quantum algorithms based on mixed states with negligible entanglement has renewed the interest on alternative measures of quantum correlations. Here we discuss a general measure of quantum correlations for composite systems based on generalized entropic functions, defined as the minimum information loss due to a local measurement. For pure states, the present measure becomes an entanglement entropy, i.e., it reduces to the generalized entropy of the reduced state. However, for mixed states it can be nonzero in separable states, vanishing just for states diagonal in a general product basis, like the quantum discord. Quadratic measures of quantum correlations can be derived as particular cases of the present formalism. The minimum information loss due to a joint local measurement is also considered. The evaluation of these measures in a simple yet relevant case is also discussed.

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. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, UK (2000).

    MATH  Google Scholar 

  2. C. H. Bennett and S. J. Wiesner, Phys. Rev. Lett., 69, 2881 (1992).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. C. H. Bennett, G. Brassard, C. Crepeau, et al., Phys. Rev. Lett., 70, 1895 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. R. Josza and N. Linden, Proc. R. Soc. London A, 459, 2011 (2003).

    Article  ADS  Google Scholar 

  5. G. Vidal, Phys. Rev. Lett., 91, 147902 (2003).

    Article  ADS  Google Scholar 

  6. E. Knill and R. Laflamme, Phys. Rev. Lett., 81, 5672 (1998).

    Article  ADS  Google Scholar 

  7. A. Datta, S. T. Flammia, and C. M. Caves, Phys. Rev. A, 72, 042316 (2005).

    Article  ADS  Google Scholar 

  8. H. Ollivier and W. H. Zurek, Phys. Rev. Lett., 88, 017901 (2001).

    Article  ADS  Google Scholar 

  9. L. Henderson and V. Vedral, J. Phys. A: Math. Gen., 34, 6899 (2001).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. V. Vedral, Phys. Rev. Lett., 90, 050401 (2003).

    Article  MathSciNet  ADS  Google Scholar 

  11. A. Datta, A. Shaji, and C. M. Caves, Phys. Rev. Lett., 100, 050502 (2008).

    Article  ADS  Google Scholar 

  12. B. P. Lanyon, M. Barbieri, M. P. Almeida, and A. G. White, Phys. Rev. Lett., 101, 200501 (2008).

    Article  ADS  Google Scholar 

  13. S. Luo, Phys. Rev. A, 77, 042303 (2008).

    Article  ADS  Google Scholar 

  14. A. Shabani and D. A. Lidar, Phys. Rev. Lett., 102, 100402 (2009).

    Article  ADS  Google Scholar 

  15. M. S. Sarandy, Phys. Rev. A, 80, 022108 (2009).

    Article  ADS  Google Scholar 

  16. T. Werlang, S. Souza, F. F. Fanchini, and C. J. Villas Boas, Phys. Rev. A, 80, 024103 (2009).

    Article  ADS  Google Scholar 

  17. A. Ferraro, L. Aolita, D. Cavalcanti, et al., Phys. Rev. A, 81, 052318 (2010).

    Article  ADS  Google Scholar 

  18. B. Dakić, V. Vedral, and C. Brukner, Phys. Rev. Lett., 105, 190502 (2010).

    Article  ADS  Google Scholar 

  19. T. Werlang, C. Trippe, G. A. P. Ribeiro, and G. Rigolin, Phys. Rev. Lett., 105, 095702 (2010).

    Article  ADS  Google Scholar 

  20. L. Ciliberti, R. Rossignoli, and N. Canosa, Phys. Rev. A, 82, 042316 (2010).

    Article  MathSciNet  ADS  Google Scholar 

  21. F. Fanchini, M. F. Cornelio, M. C. de Oliveira, and A. O. Caldeira, Phys. Rev. A, 84, 012313 (2011).

    Article  ADS  Google Scholar 

  22. D. Girolami and G. Adesso, Phys. Rev. A, 83, 052108 (2011).

    Article  ADS  Google Scholar 

  23. S. Luo, Phys. Rev. A, 77, 022301 (2008).

    Article  ADS  Google Scholar 

  24. A. Datta and S. Gharibian, Phys. Rev. A, 79, 042325 (2009).

    Article  ADS  Google Scholar 

  25. S. Wu, U. V. Poulsen, and K. Molmer, Phys. Rev. A, 80, 032319 (2009).

    Article  ADS  Google Scholar 

  26. R. Rossignoli, N. Canosa, and L. Ciliberti, Phys. Rev. A, 82, 052342 (2010).

    Article  MathSciNet  ADS  Google Scholar 

  27. K. Modi, T. Paterek, W. Son, et al., Phys. Rev. Lett., 104, 080501 (2010).

    Article  MathSciNet  ADS  Google Scholar 

  28. H. Wehrl, Rev. Mod. Phys., 50, 221 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  29. A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and its Applications, Academic Press, New York (1979).

    MATH  Google Scholar 

  30. R. Bhatia, Matrix Analysis, Springer-Verlag, New York (1997).

    Book  Google Scholar 

  31. N. Canosa and R. Rossignoli, Phys. Rev. Lett., 88, 170401 (2002).

    Article  MathSciNet  ADS  Google Scholar 

  32. R. Rossignoli and N. Canosa, Phys. Rev. A, 66, 042306 (2002).

    Article  ADS  Google Scholar 

  33. C. Tsallis, J. Stat. Phys., 52, 479 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. C. Tsallis, Introduction to Nonextensive Statistical Mechanics, Springer-Verlag, New York (2009).

    MATH  Google Scholar 

  35. C. Beck and F. Schlögl, Thermodynamics of Chaotic Systems, Cambridge University Press, Cambridge, UK (1993).

    Book  Google Scholar 

  36. R. Rossignoli and N. Canosa, Phys. Rev. A, 67, 042302 (2003).

    Article  ADS  Google Scholar 

  37. V. Vedral, Rev. Mod. Phys., 74, 197 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. R. F. Werner, Phys. Rev. A, 40, 4277 (1989).

    Article  ADS  Google Scholar 

  39. P. Rungta and C. M. Caves, Phys. Rev. A, 67, 012307 (2003).

    Article  ADS  Google Scholar 

  40. P. Rungta, V. Bužek, C. M. Caves, et al., Phys. Rev. A, 64, 042315 (2001).

    Article  MathSciNet  ADS  Google Scholar 

  41. W. K. Wootters, Phys. Rev. Lett., 80, 2245 (1998).

    Article  ADS  Google Scholar 

  42. R. Rossignoli, N. Canosa, and J. M. Matera, Phys. Rev. A 77, 052322 (2008).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física - IFLP, Universidad Nacional de La Plata, C.C.67, CP:1900, La Plata, Buenos Aires, Argentina

    R. Rossignoli, N. Canosa & L. Ciliberti

  2. Comisión de Investigaciones Científicas (CIC), Calle 526, CP: 1900, La Plata, Buenos Aires, Argentina

    R. Rossignoli

  3. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Avenue Rivadavia 1917, C1033AAJ, Buenos Aires, Argentina

    N. Canosa & L. Ciliberti

Authors
  1. R. Rossignoli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Canosa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Ciliberti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Rossignoli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rossignoli, R., Canosa, N. & Ciliberti, L. Generalized measures of quantum correlations for mixed states. J Russ Laser Res 32, 467–475 (2011). https://doi.org/10.1007/s10946-011-9236-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10946-011-9236-9

Keywords

Search

Navigation