Predominance of entanglement of formation over quantum discord under quantum channels

Abstract

We present a study of the behavior of two different figures of merit for quantum correlations, entanglement of formation and quantum discord, under quantum channels showing how the former can, counterintuitively, be more resilient to such environments spoiling effects. By exploiting strict conservation relations between the two measures and imposing necessary constraints on the initial conditions we are able to explicitly show this predominance is related to build-up of the system-environment correlations.

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References

  1. 1.

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

    ADS  Article  Google Scholar 

  2. 2.

    Schrödinger, E.: Probability relations between separated systems. Proc. Camb. Philos. Soc. 32, 446–451 (1936)

    ADS  Article  Google Scholar 

  3. 3.

    Eisert, J., Plenio, M.: A comparison of entanglement measures. J. Mod. Opt. 46, 145–154 (1999)

    ADS  Google Scholar 

  4. 4.

    Życzkowski, K.: Volume of the set of separable states. II. Phys. Rev. A 60, 3496–3507 (1999)

    MathSciNet  ADS  Article  Google Scholar 

  5. 5.

    Virmani, S., Plenio, M.B.: Ordering states with entanglement measures. Phys. Lett. A 268, 31–34 (2000)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  6. 6.

    Miranowicz, A., Grudka, A.: Ordering two-qubit states with concurrence and negativity. Phys. Rev. A 70, 032326 (2004)

    ADS  Article  Google Scholar 

  7. 7.

    Okrasa, M., Walczak, Z.: On two-qubit states ordering with quantum discords. EPL 98, 40003 (2012)

    ADS  Article  Google Scholar 

  8. 8.

    Giorgi, G.L., Bellomo, B., Galve, F., Zambrini, R.: Genuine quantum and classical correlations in multipartite systems. Phys. Rev. Lett. 107, 190501 (2011)

    ADS  Article  Google Scholar 

  9. 9.

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

    ADS  Article  Google Scholar 

  10. 10.

    Gillet, J., Agarwal, G.S., Bastin, T.: Tunable entanglement, antibunching, and saturation effects in dipole blockade. Phys. Rev. A 81, 013837 (2010)

    ADS  Article  Google Scholar 

  11. 11.

    Osborne, T.J., Nielsen, M.A.: Entanglement in a simple quantum phase transition. Phys. Rev. A 66, 032110 (2002)

    MathSciNet  ADS  Article  Google Scholar 

  12. 12.

    Maziero, J., Cleri, L.C., Serra, R.M., Sarandy, M.S.: Long-range quantum discord in critical spin systems. Phys. Lett. A 376, 1540–1544 (2012)

    ADS  MATH  Article  Google Scholar 

  13. 13.

    Campbell, S., Mazzola, L., Paternostro, M.: Global quantum correlation in the Ising model. Int. J. Quant. Inf. 9, 1685–1699 (2011)

    MathSciNet  MATH  Article  Google Scholar 

  14. 14.

    Sarovar, M., Ishizaki, A., Fleming, G.R., Whaley, K.B.: Quantum entanglement in photosynthetic light-harvesting complexes. Nat. Phys. 6, 462–467 (2010)

    Article  Google Scholar 

  15. 15.

    Lorenzo, S., Plastina, F., Paternostro, M.: Role of environmental correlations in the non-Markovian dynamics of a spin system. Phys. Rev. A 84, 032124 (2011)

    ADS  Article  Google Scholar 

  16. 16.

    Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  17. 17.

    Maziero, J., Werlang, T., Fanchini, F.F., Celeri, L.C., Serra, R.M.: System-reservoir dynamics of quantum and classical correlations. Phys. Rev. A 81, 022116 (2010)

    ADS  Article  Google Scholar 

  18. 18.

    Maziero, J., Cleri, L.C., Serra, R.M., Vedral, V.: Classical and quantum correlations under decoherence. Phys. Rev. A. 80, 044102 (2009)

    MathSciNet  ADS  Article  Google Scholar 

  19. 19.

    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  20. 20.

    Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655–1707 (2012)

    ADS  Article  Google Scholar 

  21. 21.

    Streltsov, A., Kampermann, H., Bruß, D.: Behavior of quantum correlations under local noise. Phys. Rev. Lett. 107, 170502 (2011)

    ADS  Article  Google Scholar 

  22. 22.

    Ciccarello, F., Giovannetti, V.: Creating quantum correlations through local nonunitary memoryless channels. Phys. Rev. A 85, 010102(R) (2012)

    ADS  Google Scholar 

  23. 23.

    Campbell, S., et al.: Propagation of nonclassical correlations across a quantum spin chain. Phys. Rev. A 84, 052316 (2011)

    ADS  Article  Google Scholar 

  24. 24.

    Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    ADS  Article  Google Scholar 

  25. 25.

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

    MathSciNet  ADS  MATH  Article  Google Scholar 

  26. 26.

    Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323, 598–601 (2009)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  27. 27.

    Ferraro, A., Aolita, L., Cavalcanti, D., Cucchietti, F.M., Acin, A.: Almost all quantum states have nonclassical correlations. Phys. Rev. A 81, 052318 (2010)

    ADS  Article  Google Scholar 

  28. 28.

    Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J.: Robustness of quantum discord to sudden death. Phys. Rev A 80, 024103 (2009)

    ADS  Article  Google Scholar 

  29. 29.

    Girolami, D., Adesso, G.: Interplay between computable measures of entanglement and other quantum correlations. Phys. Rev. A 84, 052110 (2011)

    ADS  Article  Google Scholar 

  30. 30.

    Fanchini, F.F., Cornelio, M.F., de Oliveira, M.C., Caldeira, A.O.: Conservation law for distributed entanglement of formation and quantum discord. Phys. Rev A 84, 012313 (2011)

    ADS  Article  Google Scholar 

  31. 31.

    Piani, M., Adesso, G.: Quantumness of correlations revealed in local measurements exceeds entanglement. Phys. Rev. A 85, 040301(R) (2012)

    ADS  Article  Google Scholar 

  32. 32.

    Paini, M., et al.: All nonclassical correlations can be activated into distillable entanglement. Phys. Rev. Lett. 106, 220403 (2011)

    ADS  Article  Google Scholar 

  33. 33.

    Streltsov, A., Kampermann, H., Bruß, D.: Linking quantum discord to entanglement in a measurement. Phys. Rev. Lett. 106, 160401 (2011)

    ADS  Article  Google Scholar 

  34. 34.

    Streltsov, A., Kampermann, H., Bruß, D.: Characterizing quantumness via entanglement creation. Int. J. Quant. Inform. 9, 1701–1713 (2011)

    Article  Google Scholar 

  35. 35.

    Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wooters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824–3851 (1996)

    MathSciNet  ADS  Article  Google Scholar 

  36. 36.

    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)

    ADS  Article  Google Scholar 

  37. 37.

    Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  38. 38.

    Al-Qasimi, A., James, D.F.V.: Comparison of the attempts of quantum discord and quantum entanglement to capture quantum correlations. Phys. Rev. A 83, 032101 (2011)

    ADS  Article  Google Scholar 

  39. 39.

    Girolami, D., Paternostro, M., Adesso, G.: Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states. J. Phys. A Math. Theor. 44, 352002 (2011)

    Article  Google Scholar 

  40. 40.

    Giorgi, G.L.: Monogamy properties of quantum and classical correlations. Phys. Rev. A 84, 054301 (2011)

    ADS  Article  Google Scholar 

  41. 41.

    Prabhu, R., Pati, A.K., De, A.S., Sen, U.: Conditions for monogamy of quantum correlations: Greenberger-Horne-Zeilinger versus W states. Phys. Rev. A 85, 040102(R) (2012)

    ADS  Article  Google Scholar 

  42. 42.

    Werner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)

    ADS  Article  Google Scholar 

  43. 43.

    Cornelio, M.F., et al.: Emergence of the pointer basis through the dynamics of correlations. Phys. Rev. Lett 109, 190402 (2012)

    ADS  Article  Google Scholar 

  44. 44.

    Piani, M.: Problem with geometric discord. Phys. Rev. A 86, 034101 (2012)

    ADS  Article  Google Scholar 

  45. 45.

    Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)

    ADS  Article  Google Scholar 

  46. 46.

    Chuan, T.K., Maillard, J., Modi, K., Paterek, T., Paternostro, M., Piani, M.: Quantum discord bounds the amount of distributed entanglement. Phys. Rev. Lett. 109, 070501 (2012)

    ADS  Article  Google Scholar 

  47. 47.

    Streltsov, A., Kampermann, H., Bruß, D.: Quantum cost for sending entanglement. Phys. Rev. Lett. 108, 250501 (2012)

    ADS  Article  Google Scholar 

  48. 48.

    Ma, Z.-H., Chen, Z.-H., Fanchini, F.F.: Multipartite quantum correlations in open quantum systems. arxiv:1207.4095

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Acknowledgments

The author greatly acknowledges fruitful discussions and exchanges with Drs. Mauro Paternostro, Tomasz Paterek, Laura Mazzola, Thomas Busch, Gianluca Giorgi and Dave Rea.

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Correspondence to Steve Campbell.

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Campbell, S. Predominance of entanglement of formation over quantum discord under quantum channels. Quantum Inf Process 12, 2623–2636 (2013). https://doi.org/10.1007/s11128-013-0548-2

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Keywords

  • Entanglement
  • Open systems
  • Quantum discord
  • Quantum correlations