Skip to main content

Advertisement

Springer Nature Link
Log in

Weak quantum discord

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Originally introduced as the difference between two possible forms of quantum mutual information, quantum discord has posteriorly been shown to admit a formulation according to which it measures a distance between the state under scrutiny and the closest projectively measured (non-discordant) state. Recently, it has been shown that quantum discord results in higher values when projective measurements are substituted by weak measurements. This sounds paradoxical since weaker measurements should imply weaker disturbance and, thus, a smaller distance. In this work, we solve this puzzle by presenting a quantifier and an underlying interpretation for what we call weak quantum discord. As a by-product, we introduce the notion of symmetrical weak quantum discord.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. Of course, the WQD also vanishes for \(\varepsilon \rightarrow 0\), but this trivial limit is not included in the statement of Theorem 1.

  2. Of course, the SyWQD will also vanishes for \((\varepsilon ',\varepsilon )\rightarrow (0,0)\).

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  MATH  ADS  Google Scholar 

  2. Schrödinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 555–563 (1935)

    Article  MATH  ADS  Google Scholar 

  3. Bell, J.S.: On the Einstein-Podolsky-Rosen paradox. Physics 1, 195 (1964)

    Article  MathSciNet  Google Scholar 

  4. Horodecki, R., Horodecki, P., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247 (2000)

    Article  MATH  ADS  Google Scholar 

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

    MATH  Google Scholar 

  7. Galindo, A., Martín-Delgado, M.A.: Information and computation: classical and quantum aspects. Rev. Mod. Phys. 74, 347 (2002)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  8. Buhrman, H., Cleve, R., Massar, S., de Wolf, R.: Nonlocality and communication complexity. Rev. Mod. Phys. 82, 665 (2010)

    Article  ADS  Google Scholar 

  9. Popescu, S.: Bell’s inequalities versus teleportation: what is nonlocality? Phys. Rev. Lett. 72, 797 (1994)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  10. Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  11. Angelo, R.M., Ribeiro, A.D.: Wave-particle duality: an information-based approach. Found. Phys. 45, 1407 (2015)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  12. Bilobran, A.L.O., Angelo, R.M.: A measure of physical reality. Europhys. Lett. 112, 40005 (2015)

    Article  ADS  Google Scholar 

  13. Dieguez, P.R., Angelo, R.M.: Information-reality complementarity: the role of measurements and quantum reference frames. Phys. Rev. A 97, 022107 (2018)

    Article  ADS  Google Scholar 

  14. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 17901 (2001)

    Article  MATH  Google Scholar 

  15. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math. Gen. 34, 6899 (2001)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  16. Céleri, L.C., Maziero, J., Serra, R.M.: Theoretical and experimental aspects of quantum discord and related measures. Int. J. Quantum Inf. 9, 1837–1873 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wiseman, H.M., Jones, S.J., Doherty, A.C.: Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen Paradox. Phys. Rev. Lett. 98, 140402 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  18. Cavalcanti, E.G., Jones, S.J., Wiseman, H.M., Reid, M.D.: Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox. Phys. Rev. A 80, 032112 (2009)

    Article  ADS  Google Scholar 

  19. Costa, A.C.S., Angelo, R.M.: Quantification of Einstein-Podolski-Rosen steering for two-qubit states. Phys. Rev. A 93, 020103(R) (2016)

    Article  ADS  Google Scholar 

  20. Dakić, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  MATH  ADS  Google Scholar 

  21. Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011)

    Article  ADS  Google Scholar 

  22. Rossignoli, R., Canosa, N., Ciliberti, L.: Generalized entropic measures of quantum correlations. Phys. Rev. A 82, 052342 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  23. Costa, A.C.S., Angelo, R.M.: Bayes’ rule, generalized discord, and nonextensive thermodynamics. Phys. Rev. A 87, 032109 (2013)

    Article  ADS  Google Scholar 

  24. Maudlin, T.: In: Hull, D., Forbes, M., Okruhlik, K. (eds.) Proceedings of the 1992 Meeting of the Philosophy of Science Association. Philosophy of Science Association, East Lansing, MI, 1992, vol. 1, pp. 404–417 (1992)

  25. Brassard, G., Cleve, R., Tapp, A.: Cost of exactly simulating quantum entanglement with classical communication. Phys. Rev. Lett. 83, 1874 (1999)

    Article  ADS  Google Scholar 

  26. Steiner, M.: Towards quantifying non-local information transfer: finite-bit non-locality. Phys. Lett. A 270, 239 (2000)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  27. Kaszlikowski, D., Gnacinski, P., Zukowski, M., Miklaszewski, W., Zeilinger, A.: Violations of local realism by two entangled \(N\)-dimensional systems are stronger than for two qubits. Phys. Rev. Lett. 85, 4418 (2000)

    Article  Google Scholar 

  28. Bacon, D., Toner, B.F.: Bell inequalities with auxiliary communication. Phys. Rev. Lett. 90, 157904 (2003)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  29. Branciard, C., Gisin, N.: Quantifying the nonlocality of Greenberger-Horne-Zeilinger quantum correlations by a bounded communication simulation protocol. Phys. Rev. Lett. 107, 020401 (2011)

    Article  ADS  Google Scholar 

  30. Laskowski, W., Ryu, J., Zukowsky, M.: Noise resistance of the violation of local causality for pure three-qutrit entangled states. J. Phys. A 47, 424019 (2014)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  31. Fonseca, E.A., Parisio, F.: Measure of nonlocality which is maximal for maximally entangled qutrits. Phys. Rev. A 92, 030101(R) (2015)

    Article  ADS  Google Scholar 

  32. Costa, A.C.S., Beims, M.W., Angelo, R.M.: Generalized discord, entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in two-qubit systems under (non-)Markovian channels: hierarchy of quantum resources and chronology of deaths and births. Physica A (Amsterdam, Neth.) 461, 469 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  33. Gomes, V.S., Angelo, R.M.: Nonanomalous realism-based measure of nonlocality. Phys. Rev. A 97, 012123 (2018)

    Article  ADS  Google Scholar 

  34. Modi, K., Paterek, T., Son, W., Vedral, V.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  35. Aharonov, Y., Albert, D.Z., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351 (1998)

    Article  ADS  Google Scholar 

  36. Aharonov, Y., Cohen, E., Elitzur, A.C.: Foundations and applications of weak quantum measurements. Phys. Rev. A 89, 052105 (2014)

    Article  ADS  Google Scholar 

  37. Oreshkov, O., Brun, T.A.: Weak measurements are universal. Phys. Rev. Lett. 95, 1104909 (2005)

    Article  Google Scholar 

  38. Li, L., Wang, Q.W., Shen, S.Q., Li, M.: Geometric measure of quantum discord with weak measurements. Quantum Inf. Process. 15, 291–300 (2016)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  39. Singh, U., Pati, A.K.: Quantum discord with weak measurements. Ann. Phys. 343, 141–152 (2014)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  40. Wang, Y.K., Ma, T., Fan, H., Fei, S.M., Wang, Z.X.: Super-quantum correlation and geometry for Bell-diagonal states with weak measurements. Quantum Inf. Process. 13, 283–297 (2014)

    Article  MATH  ADS  Google Scholar 

  41. Hu, M.L., Fan, H., Tian, D.P.: Role of weak measurements on states ordering and monogamy of quantum correlation. Int. J. Theor. Phys. 54, 62–71 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  42. Li, T., Ma, T., Wang, Y., Fei, S., Wang, Z.: Super quantum discord for X-type states. Int. J. Theor. Phys. 54, 680–688 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  43. Jing, N., Yu, B.: Super quantum discord for general two qubit X states. Quantum Inf. Process. 16, 99 (2017)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  44. Xiang, M., Jing, J.: Quantum discord and inferior "geometric discord" based on weak measurement in noninertial frames. J. Quantum Inf. Sci. 4, 54 (2014)

    Article  Google Scholar 

  45. Vidal, G.: Entanglement monotones. J. Mod. Opt. 47, 355 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  46. Brodutch, A., Modi, K.: Criteria for measures of quantum correlations. Quantum Inf. Comput. 12, 0721 (2012)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

P. R. Dieguez and R. M. Angelo, respectively, acknowledge financial support from the Brazilian Agencies CAPES and CNPq. This work was partially supported by the National Institute for Science and Technology of Quantum Information (INCT-IQ/CNPq, Brazil).

Author information

Authors and Affiliations

  1. Department of Physics, Federal University of Paraná, P.O. Box 19044, Curitiba, Paraná, 81531-980, Brazil

    P. R. Dieguez & R. M. Angelo

Authors
  1. P. R. Dieguez
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. R. M. Angelo
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to R. M. Angelo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dieguez, P.R., Angelo, R.M. Weak quantum discord. Quantum Inf Process 17, 194 (2018). https://doi.org/10.1007/s11128-018-1963-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1963-1

Keywords