Skip to main content
SpringerLink
Log in

Gaussian quantum discord and the monogamy relation in de Sitter space

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We study the influence of a two-mode Gaussian state under the Gaussian channel that describes the curvature effect in de Sitter space. Interestingly, the classical correlation may be unaffected by the curvature effect, while the quantum discord generally vanishes in the limit of infinite curvature. Under the action of curvature effect, the symmetry of both the classical correlation and quantum discord is destroyed. We obtain a useful monogamy relation for correlations between causally disconnected open charts, which means that quantum discord and classical correlation can convert each other but the total correlation is conserved in de Sitter space.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data availability

This manuscript has no associated data or the data will not be deposited. [Authors comment: All data included in this study are available upon request by contact with the corresponding author Hao-Sheng Zeng.]

References

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

    MATH  Google Scholar 

  2. Wilde, M.M.: Quantum Information Theory. Cambridge University Press, Cambridge (2013)

    Book  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Wu, S.M., Zeng, H.S.: Schwinger effect of Gaussian correlations in constant electric fields. Class. Quantum Grav. 37, 115003 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. 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 (2012)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. 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)

    Article  ADS  Google Scholar 

  9. Wu, S.M., Li, Z.C., Zeng, H.S.: Multipartite coherence and monogamy relationship under the Unruh effect in an open system. Quantum Inf. Process. 20, 277 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  10. Peres, A., Terno, D.R.: Quantum information and relativity theory. Rev. Mod. Phys. 76, 93 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. 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 

  12. 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 

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

    Article  ADS  Google Scholar 

  14. Martín-Martínez, E., Fuentes, I.: Redistribution of particle and antiparticle entanglement in noninertial frames. Phys. Rev. A 83, 052306 (2011)

    Article  ADS  Google Scholar 

  15. Dai, Y., Shen, Z., Shi, Y.: Quantum entanglement in three accelerating qubits coupled to scalar fields. Phys. Rev. D 94, 025012 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  16. Wang, J., Jing, J., 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 

  17. Brown, E.G., Cormier, K., Martín-Martínez, E., Mann, R.B.: Vanishing geometric discord in noninertial frames. Phys. Rev. A 86, 032108 (2012)

    Article  ADS  Google Scholar 

  18. Adesso, G., Ragy, S., Girolami, D.: Continuous variable methods in relativistic quantum information: characterization of quantum and classical correlations of scalar field modes in noninertial frames. Class. Quantum Grav. 29, 224002 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Ball, J.L., Fuentes-Schuller, I., Schuller, F.P.: Entanglement in an expanding spacetime. Phys. Lett. A 359, 550 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Fuentes, I., Mann, R.B., Martín-Martínez, E., Moradi, S.: Entanglement of Dirac fields in an expanding spacetime. Phys. Rev. D 82, 045030 (2010)

    Article  ADS  Google Scholar 

  21. Martín-Martínez, E., Menicucci, N.C.: Cosmological quantum entanglement. Class. Quantum Grav. 29, 224003 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Nambu, Y., Ohsumi, Y.: Classical and quantum correlations of scalar field in the inflationary universe. Phys. Rev. D 84, 044028 (2011)

    Article  ADS  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. Li, T., Zhang, B., You, L.: Would quantum entanglement be increased by anti-Unruh effect? Phys. Rev. D 97, 045005 (2018)

    Article  ADS  Google Scholar 

  25. Wu, S.M., Li, Z.C., Zeng, H.S.: Quantum steering between two accelerated parties. Laser Phys. Lett. 17, 035202 (2020)

    Article  ADS  Google Scholar 

  26. Tian, Z., Jing, J., Dragan, A.: Analog cosmological particle generation in a superconducting circuit. Phys. Rev. D 95, 125003 (2017)

    Article  ADS  Google Scholar 

  27. Wu, S.M., Zeng, H.S.: Genuine tripartite nonlocality and entanglement in curved spacetime. Eur. Phys. J. C 82, 4 (2022)

    Article  ADS  Google Scholar 

  28. Wu, S.M., Zeng, H.S., Cao, H.M.: Quantum coherence and distribution of N-partite bosonic fields in noninertial frame. Class. Quantum Grav. 38, 185007 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Torres-Arenasa, A.J., Dong, Q., Sun, G.H., Qiang, W.C., Dong, S.H.: Entanglement measures of W-state in noninertial frames. Phy. Lett. B 789, 93 (2019)

    Article  ADS  Google Scholar 

  30. Ocampo, D.M., Ramírez, J.C.S., Yáñez-Márquez, C., Sun, G.H.: Entanglement measures of a pentapartite W-class state in the noninertial frame. Quantum Inf. Process. 21, 46 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  31. Sanchez, M.A.M., Sun, G.H., Dong, S.H.: Quantum discord of the Werner state in noninertial frames. Phys. Scr. 95, 115102 (2020)

    Article  ADS  Google Scholar 

  32. Wu, S.M., Cai, Y.T., Peng, W.J., Zeng, H.S.: Genuine N-partite entanglement and distributed relationships in the background of dilation black holes. Eur. Phys. J. C 82, 412 (2022)

    Article  ADS  Google Scholar 

  33. Sasaki, M., Tanaka, T., Yamamoto, K.: Euclidean vacuum mode functions for a scalar field on open de Sitter space. Phys. Rev. D 51, 2979 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  34. Wen, C., Wang, J., Jing, J.: Quantum steering for continuous variable in de Sitter space. Eur. Phys. J. C 80, 78 (2020)

    Article  ADS  Google Scholar 

  35. Wang, J., Wen, C., Chen, S., Jing, J.: Generation of genuine tripartite entanglement for continuous variables in de Sitter space. Phys. Lett. B 800, 135109 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  36. Maldacena, J., Pimentel, G.L.: Entanglement entropy in de Sitter space. J. High Energy Phys. 02, 038 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Kanno, S., Shock, J.P., Soda, J.: Quantum discord in de Sitter space. Phys. Rev. D 94, 125014 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  38. Kanno, S., Murugan, J., Shock, J.P., Soda, J.: Entanglement entropy of \(\alpha \)-vacua in de Sitter space. J. High Energy Phys. 07, 072 (2014)

    Article  ADS  Google Scholar 

  39. Albrecht, A., Kanno, S., Sasaki, M.: Quantum entanglement in de Sitter space with a wall and the decoherence of bubble universes. Phys. Rev. D 97, 083520 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  40. Matsumura, A., Nambu, Y.: Large scale quantum entanglement in de Sitter spacetime. Phys. Rev. D 98, 025004 (2018)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  42. Braunstein, S.L., van Loock, P.: Quantum information with continuous variables. Rev. Mod. Phys. 77, 513 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. Buono, D., Nocerino, G., Porzio, A., Solimeno, S.: Experimental analysis of decoherence in continuous-variable bipartite systems. Phys. Rev. A 86, 042308 (2012)

    Article  ADS  Google Scholar 

  44. He, Q.Y., Gong, Q.H., Reid, M.D.: Classifying directional Gaussian entanglement, Einstein–Podolsky–Rosen steering, and discord. Phys. Rev. Lett. 114, 060402 (2015)

    Article  ADS  Google Scholar 

  45. Adesso, G., Serafini, A., Illuminati, F.: Extremal entanglement and mixedness in continuous variable systems. Phys. Rev. A 70, 022318 (2004)

    Article  ADS  Google Scholar 

  46. Adesso, G., Datta, A.: Quantum versus classical correlations in Gaussian states. Phys. Rev. Lett. 105, 030501 (2010)

    Article  ADS  Google Scholar 

  47. Adesso, G., Girolami, D., Serafini, A.: Measuring Gaussian quantum information and correlations using the Rényi entropy of order 2. Phys. Rev. Lett. 109, 190502 (2012)

    Article  ADS  Google Scholar 

  48. Adesso, G., Ragy, S., Lee, A.R.: Continuous variable quantum information: Gaussian states and beyond. Open Syst. Inf. Dyn. 21, 1440001 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  49. Adesso, G., Fuentes-Schuller, I., Ericsson, M.: Continuous-variable entanglement sharing in noninertial frames. Phys. Rev. A 76, 062112 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  50. 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  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  52. Terashima, H.: Entanglement entropy of the black hole horizon. Phys. Rev. D 61, 104016 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  53. Simon, R.: Peres–Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2726 (2000)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 1217050862, 11275064), and 2021BSL013.

Author information

Authors and Affiliations

  1. Department of Physics, Liaoning Normal University, Dalian, 116029, China

    Shu-Min Wu

  2. Department of Physics, Hunan Normal University, Changsha, 410081, Hunan, China

    Hao-Sheng Zeng

  3. Department of Physics, Yangtze University, Jingzhou, 434023, China

    Tonghua Liu

Authors
  1. Shu-Min Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao-Sheng Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tonghua Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Shu-Min Wu or Hao-Sheng Zeng.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, SM., Zeng, HS. & Liu, T. Gaussian quantum discord and the monogamy relation in de Sitter space. Quantum Inf Process 21, 299 (2022). https://doi.org/10.1007/s11128-022-03632-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-022-03632-4

Keywords

Search

Navigation