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System–environment dynamics of GHZ-like states in noninertial frames

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Abstract

Quantum coherence, quantum entanglement and quantum nonlocality are important resources in quantum information processing. However, decoherence happens when a quantum system interacts with the external environments. We study the dynamical evolution of the three-qubit GHZ-like states in noninertial frame when one and/or two qubits undergo decoherence. Under the amplitude damping channel, we show that the quantum decoherence and the Unruh effect may have quite different influences on the initial state. Moreover, the genuine tripartite entanglement and the quantum coherence may suffer sudden death during the evolution. The quantum coherence is most resistant to the quantum decoherence and the Unruh effect and then comes the quantum entanglement and the quantum nonlocality which is most fragile among the three. The results provide a new research perspective for relativistic quantum informatics.

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References

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)

    Article  ADS  Google Scholar 

  3. Streltsov, A., Adesso, G., Plenio, M.B.: Colloquium: quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  4. Hu, M.L., Hu, X., Wang, J.C., Peng, Y., Zhang, Y.R., Fan, H.: Quantum coherence and geometric quantum discord. Phys. Rep. 762, 1 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)

    Article  ADS  Google Scholar 

  7. Giulini, D., Joos, E., Kiefer, C., Kupsch, J., Stamatescu, I.O., Zeh, H.D.: Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin (1996)

    Book  MATH  Google Scholar 

  8. Schlosshauer, M.A.: Decoherence and the Quantum-to-classical Transition. Springer, Berlin (2007)

    Google Scholar 

  9. Brune, M., Hagley, E., Dreyer, J., Maitre, X., Maali, A., Wunderlich, C., Raimond, J.M., Haroche, S.: Observing the progressive decoherence of the meter in a quantum measurement. Phys. Rev. Lett. 77, 4887 (1996)

    Article  ADS  Google Scholar 

  10. Myatt, C.J., King, B.E., Turchette, Q.A., Sackett, C.A., Kielpinski, D., Itano, W.M., Monroe, C., Wineland, D.J.: Experimental entanglement of four particles. Nature 403, 269 (2000)

    Article  ADS  Google Scholar 

  11. Alsing, P.M., Milburn, G.J.: Teleportation with a uniformly accelerated partner. Phys. Rev. Lett. 91, 180404 (2003)

    Article  ADS  Google Scholar 

  12. 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 

  13. 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 

  14. Wang, J., Pan, Q., Chen, S., Jing, J.: Entanglement of coupled massive scalar field in background of dilaton black hole. Phys. Lett. B 677, 186 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  15. Martín-Martínez, E., Garay, L.J., León, J.: Unveiling quantum entanglement degradation near a Schwarzschild black hole. Phys. Rev. D 82, 064006 (2010)

    Article  ADS  Google Scholar 

  16. Wang, J., Pan, Q., Jing, J.: Entanglement redistribution in the Schwarzschild spacetime. Phys. Lett. B 692, 202 (2010)

    Article  ADS  Google Scholar 

  17. Martín-Martínez, E., Garay, L.J., León, J.: Quantum entanglement produced in the formation of a black hole. Phys. Rev. D 82, 064028 (2010)

    Article  ADS  Google Scholar 

  18. Wang, J., Jing, J.: Quantum decoherence in noninertial frames. Phys. Rev. A 82, 032324 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Khan, S., Khan, M.K.: Open quantum systems in noninertial frames. J. Phys. A: Math. Theor. 44, 045305 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Nasr Esfahani, B., Shamirzaie, M., Soltani, M.: Reduction of entanglement degradation in Einstein–Gauss–Bonnet gravity. Phys. Rev. D 84, 025024 (2011)

    Article  ADS  Google Scholar 

  22. Mann, R.B., Ralph, T.C.: Relativistic quantum information. Class. Quantum Gravity 29, 220301 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  23. Tian, Z., Jing, J.: Geometric phase of two-level atoms and thermal nature of de Sitter spacetime. J. High Energy Phys. 04, 109 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  24. 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 

  25. Tian, Z., Jing, J.: Distinguishing de Sitter universe from thermal Minkowski spacetime by Casimir–Polder-like force. J. High Energy Phys. 07, 089 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  27. 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 

  28. Friis, N.: Reasonable fermionic quantum information theories require relativity. New J. Phys. 18, 033014 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Liu, X., Tian, Z., Wang, J., Jing, J.: Radiative process of two entanglement atoms in de Sitter spacetime. Phys. Rev. D 97, 105030 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  30. Qiang, W.C., Sun, G.H., Dong, Q., Dong, S.H.: Genuine multipartite concurrence for entanglement of Dirac fields in noninertial frames. Phys. Rev. A 98, 022320 (2018)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Wu, S.M., Li, Z.C., Zeng, H.S.: Quantum coherence of multipartite w-state in a Schwarzschild spacetime. EPL 129, 40002 (2020)

    Article  ADS  Google Scholar 

  34. Wang, J., Zhang, L., Chen, S., Jing, J.: Estimating the Unruh effect via entangled many-body probes. Phys. Lett. B 802, 135239 (2020)

    Article  MathSciNet  Google Scholar 

  35. Liu, Q., Wen, C., Tian, Z., Jing, J., Wang, J.: Gravity-enhanced quantum spatial target detection. Phys. Rev. A 105, 062428 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  36. 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 

  37. Xiao, L., Wen, C., Jing, J., Wang, J.: Black-box estimation of expanding parameter for de Sitter universe. Eur. Phys. J. C 82, 684 (2022)

    Article  ADS  Google Scholar 

  38. Li, L.J., Ming, F., Song, X.K., Ye, L., Wang, D.: Quantumness and entropic uncertainty in curved space–time. Eur. Phys. J. C 82, 726 (2022)

    Article  ADS  Google Scholar 

  39. Wu, S.M., Zeng, H.S., Liu, T.: Genuine multipartite entanglement subject to the Unruh and anti-Unruh effects. New J. Phys. 24, 073004 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  40. Szypulski, J.A., Grochowski, P.T., Debski, K., Dragan, A.: Effect of relativistic acceleration on tripartite entanglement in Gaussian states. arXiv:2112.07250 (2021)

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

    Article  ADS  Google Scholar 

  42. Hawking, S.W.: Black hole explosions? Nature 248, 30 (1974)

    Article  ADS  MATH  Google Scholar 

  43. Aspachs, M., Adesso, G., Fuentes, I.: Optimal quantum estimation of the Unruh–Hawking effect. Phys. Rev. Lett. 105, 151301 (2010)

    Article  ADS  Google Scholar 

  44. Bruschi, D.E., Louko, J., Martn-Martnez, E., Dragan, A., Fuentes, I.: Unruh effect in quantum information beyond the single-mode approximation. Phys. Rev. A 82, 042332 (2010)

    Article  ADS  Google Scholar 

  45. 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 

  46. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722 (1997)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Zhang, T., Wang, X., Fei, S.M.: Hawking effect can generate physically inaccessible genuine tripartite nonlocality. Eur. Phys. J. C 83, 607 (2023)

    Article  ADS  Google Scholar 

  49. Zhang, W., Jing, J.: Multipartite entanglement for open system in noninertial frames. arXiv:1103.4903v1 (2011)

  50. Zeng, H.S., Cao, H.M.: Distribution and evolution of quantum coherence for open multi-qubit systems in noninertial frames. Ann. Phys. (Berlin) 533, 2000606 (2021)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. Kim, K.I., Pak, M.C., An, O.S., Ri, U.G., Ko, M.C., Kim, N.C.: Quantum entanglement and coherence of tripartite W state for Dirac fields under noisy channels in non-inertial frames. Phys. Scr. 97, 075101 (2022)

    Article  ADS  Google Scholar 

  53. Salles, A., de Melo, F., Almeida, M.P., Hor-Meyll, M., Walborn, S.P., SoutoRibeiro, P.H., Davidovich, L.: Experimental investigation of the dynamics of entanglement: sudden death, complementarity, and continuous monitoring of the environment. Phys. Rev. A 78, 022322 (2008)

    Article  ADS  Google Scholar 

  54. Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. Yu, T., Eberly, J.H.: Quantum open system theory: bipartite aspects. Phys. Rev. Lett. 97, 140403 (2006)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  57. Carmichael, H.: An Open Systems Approach to Quantum Optics. Springer, Berlin (1993)

    Book  MATH  Google Scholar 

  58. Kraus, K.: States, Effects and Operations: Fundamental Notions of Quantum Theory. Springer, Berlin (1983)

    Book  MATH  Google Scholar 

  59. Choi, M.D.: Completely positive linear maps on complex matrices. Linear Algebr. Appl. 10, 285 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  60. Leung, D.W.: Choi’s proof as a recipe for quantum process tomography. J. Math. Phys. 44, 528 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  61. 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)

    Article  ADS  Google Scholar 

  62. Wang, K., Zheng, Z.J.: Violation of svetlichny inequality in triple jaynes-cummings models. Sci. Rep. 10, 6621 (2020)

    Article  ADS  Google Scholar 

  63. Svetlichny, G.: Distinguishing three-body from two-body nonseparability by a Bell-type inequality. Phys. Rev. D 35, 3066 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  64. Ma, Z.H., Chen, Z.H., Chen, J.L., Spengler, C., Gabriel, A., Huber, M.: Measure of genuine multipartite entanglement with computable lower bounds. Phys. Rev. A 83, 062325 (2011)

    Article  ADS  Google Scholar 

  65. Hashemi Rafsanjani, S.M., Huber, M., Broadbent, C.J., Eberly, J.H.: Genuinely multipartite concurrence of N-qubit X matrices. Phys. Rev. A 86, 062303 (2012)

    Article  ADS  Google Scholar 

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Acknowledgements

This work is supported by the Hainan Provincial Natural Science Foundation of China under Grant No. 121RC539; the National Natural Science Foundation of China (NSFC) under Grant Nos. 12171044, 12204137 and 12075159; the specific research fund of the Innovation Platform for Academicians of Hainan Province under Grant No. YSPTZX202215; and Beijing Natural Science Foundation (Grant No. Z190005).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, China

    Tinggui Zhang

  2. School of Physics and Electronic Engineering, Hainan Normal University, Haikou, 571158, China

    Hong Yang

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei

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  1. Tinggui Zhang
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  2. Hong Yang
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Zhang, T., Yang, H. & Fei, SM. System–environment dynamics of GHZ-like states in noninertial frames. Quantum Inf Process 22, 331 (2023). https://doi.org/10.1007/s11128-023-04081-3

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