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Probing the entanglement distillability responses to the Unruh effect and prepared states

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Abstract

How the Unruh–Hawking effect and prepared states influence the entanglement distillability of a free Dirac field is investigated by using the Werner and Horodecki states. It is found that Werner and Horodecki states will be converted from distillable into the separate in the noninertial frame. The parameter \(\alpha \) of the generic entangled states has a different effect on Werner-like and Horodecki-like states. For the Werner-like states, although the parameter \(\alpha \) influences the entanglement, it does not change the range of the parameter \(F\) where the entanglement distillability of the Werner-like states is possible. For the Horodecki-like states, the parameter \(\alpha \) not only influences the entanglement but also changes the range of the parameter \(P\) where the entanglement distillability of Horodecki-like states can be achieved.

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References

  1. Song, W., Chen, L., Zhu, S.L.: Sudden death of distillability in qutrit–qutrit systems. Phys. Rev. A 80, 012331 (2009)

    Article  ADS  Google Scholar 

  2. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  3. Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. Horodecki, M., Horodecki, P., Horodecki, R.: Inseparable two spin-12 density matrices can be distilled to a singlet form. Phys. Rev. Lett. 78, 574 (1997)

    Article  ADS  Google Scholar 

  5. Horodecki, M., Horodecki, P., Horodecki, R.: Mixed-state entanglement and distillation: is there a “bound” entanglement in nature? Phys. Rev. Lett. 80, 5239 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  6. Linden, N., Massar, S., Popescu, S.: Purifying noisy entanglement requires collective measurements. Phys. Rev. Lett. 81, 3279 (1998)

    Article  ADS  Google Scholar 

  7. Kent, A.: Entangled mixed states and local purification. Phys. Rev. Lett. 81, 2839 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Acín, A.: Distillability, Bell inequalities, and multiparticle bound entanglement. Phys. Rev. Lett. 88, 027901 (2001)

    Article  ADS  Google Scholar 

  9. Clarisse, L.: Characterization of distillability of entanglement in terms of positive maps. Phys. Rev. A 71, 032332 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  10. Lamata, L., Martin-Delgado, M.A., Solano, E.: Relativity and lorentz invariance of entanglement distillability. Phys. Rev. Lett. 97, 250502 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  11. Vianna, R.O., Doherty, A.C.: Distillability of Werner states using entanglement witnesses and robust semidefinite programs. Phys. Rev. A 74, 052306 (2006)

    Article  ADS  Google Scholar 

  12. Lee, S., Joo, J., Kim, J.: Teleportation capability, distillability, and nonlocality on three-qubit states. Phys. Rev. A 76, 012311 (2007)

    Article  ADS  Google Scholar 

  13. Kwon, Y.: Asymptotic relation between Bell-inequality violations and entanglement distillability. Phys. Rev. A 82, 054104 (2010)

    Article  ADS  Google Scholar 

  14. Deng, J.F., Wang, J.C., Jing, J.L.: How the Hawking effect and prepared states affect entanglement distillability of Dirac fields. Phys. Lett. B 695, 495–500 (2011)

    Article  ADS  Google Scholar 

  15. Vertesi, T., Brunner, N.: Quantum nonlocality does not imply entanglement distillability. Phys. Rev. Lett. 108, 030403 (2012)

    Article  ADS  Google Scholar 

  16. Zhao, M., Zhao, T.G., Li, X.Q., Fei, S.M.: Entanglement detection and distillation for arbitrary bipartite systems. Quantum Inf. Proc. 12, 2861–2870 (2013)

    Article  ADS  MATH  Google Scholar 

  17. Fuentes-Schuller, I., Mann, R.B.: Alice falls into a black hole: entanglement in noninertial frames. Phys. Rev. Lett. 95, 120404 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  18. Wang, J.C., Jing, J.L.: Multipartite entanglement of fermionic systems in noninertial frames. Phys. Rev. A 83, 022314 (2011)

    Article  ADS  Google Scholar 

  19. Bradler, K.: Eavesdropping of quantum communication from a noninertial frame. Phys. Rev. A 75, 022311 (2007)

    Article  ADS  Google Scholar 

  20. Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  21. Hawking, S.W.: Breakdown of predictability in gravitational collapse. Phys. Rev. D 14, 2460 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  22. Bombelli, L., Koul, R.K., Lee, J., Sorkin, R.D.: Quantum source of entropy for black holes. Phys. Rev. D 34, 373 (1986)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  23. Xu, S., Song, X.K., Shi, J.D., Ye, L.: How the Hawking effect affects multipartite entanglement of Dirac particles in the background of a Schwarzschild black hole. Phys. Rev. D 89, 065022 (2014)

    Article  ADS  Google Scholar 

  24. Wang, J.C., Jing, J.L., Fan, H.: Quantum discord and measurement-induced disturbance in the background of dilaton black holes. Phys. Rev. D 90, 025032 (2014)

    Article  ADS  Google Scholar 

  25. He, J., Xu, S., Yu, Y., Ye, L.: Property of various correlation measures of open Dirac system with Hawking effect in Schwarzschild space-time. Phys. Lett. B 760, 322–328 (2015)

    Article  MathSciNet  Google Scholar 

  26. Wang, J.C., Deng, J.F., Jing, J.L.: Classical correlation and quantum discord sharing of Dirac fields in noninertial frames. Phys. Rev. A 81, 052120 (2010)

    Article  ADS  Google Scholar 

  27. Mehri-Dehnavi, H., Mirza, B., Mohammadzadeh, H., Rahimi, R.: Pseudo-entanglement evaluated in noninertial frames. Ann. Phys. 326, 1320 (2011)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  28. Pan, Q.Y., Jing, J.L.: Degradation of nonmaximal entanglement of scalar and Dirac fields in noninertial frames. Phys. Rev. A 77, 024302 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  29. Kwon, Y., Chang, J.: Entanglement amplification of fermionic systems in an accelerated frame. Phys. Rev. A 86, 014302 (2012)

    Article  ADS  Google Scholar 

  30. Smith, A., Mann, R.B.: Persistence of tripartite nonlocality for noninertial observers. Phys. Rev. A 86, 012306 (2012)

    Article  ADS  Google Scholar 

  31. Yao, Y., Xiao, X., Ge, L., Wang, X.G., Sun, C.P.: Quantum fisher information in noninertial frames. Phys. Rev. A 89, 042336 (2014)

    Article  ADS  Google Scholar 

  32. Metwally, N.: Teleportation of accelerated information. J. Opt. Soc. Am. B 30, 233–237 (2013)

    Article  ADS  Google Scholar 

  33. Metwally, N.: Usefulness classes of traveling entangled channels in noninertial frames. Int. J. Mod. Phys. B 27, 1350155 (2013)

  34. Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D 14, 870 (1976)

    Article  ADS  Google Scholar 

  35. Montero, M., Martın-Martınez, E.: The entangling side of the Unruh–Hawking effect. J. High Energy Phys. 07, 006 (2011)

    Article  ADS  Google Scholar 

  36. Moradi, S.: Distillability of entanglement in accelerated frames. Phys. Rev. A 79, 064301 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  37. Xiao, X., Fang, M.F.: Mixed-state entanglement in noninertial frames. J. Phys. A Math. Theor. 44, 145306 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  38. Alsing, P.M., Fuentes-Schuller, I., Mann, R.B., Tessier, T.E.: Entanglement of Dirac fields in noninertial frames. Phys. Rev. A 74, 032326 (2006)

    Article  ADS  Google Scholar 

  39. Eltschka, C., Siewert, J.: Negativity as an estimator of entanglement dimension. Phys. Rev. Lett. 111, 100503 (2013)

    Article  ADS  Google Scholar 

  40. Zyczkowski, K., Horodecki, P., Sanpera, A., Lewenstein, M.: Volume of the set of separable states. Phys. Rev. A 58, 883 (1998)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Horst, B., Bartkiewicz, K., Miranowicz, A.: Two-qubit mixed states more entangled than pure states: comparison of the relative entropy of entanglement for a given nonlocality. Phys. Rev. A 87, 042108 (2013)

    Article  ADS  Google Scholar 

  43. Bartkiexicz, K., Horst, B., Lemr, K., Miranowicz, A.: Entanglement estimation from Bell inequality violation. Phys. Rev. A 88, 052105 (2013)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Science Foundation of China under Grant Nos. 11074002 and 61275119, the Doctoral Foundation of the Ministry of Education of China under Grant No. 20103401110003, the Personal Development Foundation of Anhui Province (2008Z018), and also by the Natural Science Research Project of Education Department of Anhui Province of China under Grant No. KJ2013A205.

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Ma, W., Xu, S., He, J. et al. Probing the entanglement distillability responses to the Unruh effect and prepared states. Quantum Inf Process 14, 1411–1428 (2015). https://doi.org/10.1007/s11128-015-0936-x

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  • DOI: https://doi.org/10.1007/s11128-015-0936-x

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