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Nonequilibrium effects on quantum temporal steering

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Abstract

We investigate the quantum temporal steering (TS), measured by temporal steering robustness \(R_\mathrm{{TS}}\), of a two-level system coupling to a nonequilibrium environment, for the weak and the strong coupling regime. The impact of various environmental parameters on TS behavior is discussed in detail. In order to gain a deeper understanding of TS, we also analyze the non-Markovianity of the system. Our numerical results reveal that a nonequilibrium environment can enhance the quantum temporal steering of the two-level system, regardless of whether the system is experiencing Markovian or non-Markovian dynamics. Furthermore, a strong memory environment can significantly enhance TS as well. These findings suggest that manipulating the temporal steering of a quantum system can be achieved efficiently and effectively in a nonequilibrium environment.

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References

  1. 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 

  2. Jones, S.J., Wiseman, H.M., Doherty, A.C.: Entanglement, Einstein–Podolsky–Rosen correlations, bell nonlocality, and steering. Phys. Rev. A 76, 052116 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  3. Skrzypczyk, P., Navascués, M., Cavalcanti, D.: Quantifying Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 112, 180404 (2014)

    Article  ADS  Google Scholar 

  4. Cavalcanti, D., Skrzypczyk, P.: Quantum steering: a review with focus on semidefinite programming. Rep. Prog. Phys. 80, 024001 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  5. Piani, M., Watrous, J.: Necessary and sufficient quantum information characterization of Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 114, 060404 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  6. Sainz, A.B., Aolita, L., Brunner, N., Gallego, R., Skrzypczyk, P.: Classical communication cost of quantum steering. Phys. Rev. A 94, 012308 (2016)

    Article  ADS  Google Scholar 

  7. Händchen, V., Eberle, T., Steinlechner, S., Samblowski, A., Franz, T., Werner, R.F., Schnabel, R.: Observation of one-way Einstein–Podolsky–Rosen steering. Nature Photonics 6, 596–599 (2012)

    Article  ADS  Google Scholar 

  8. Bowles, J., Vértesi, T., Quintino, M.T., Brunner, N.: One-way Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 112, 200402 (2014)

    Article  ADS  Google Scholar 

  9. Kalaga, J.K., Leonski, W., Szczesniak, R.: Quantum steering and entanglement in three-mode triangle Bose–Hubbard system. Quantum Inf. Process. 16, 265 (2017)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  10. Wollmann, S., Walk, N., Bennet, A.J., Wiseman, H.M., Pryde, G.J.: Observation of genuine one-way Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 116, 160403 (2016)

    Article  ADS  Google Scholar 

  11. Das, D., Sasmal, S., Roy, A.: Role of maximally entangled states in the context of linear steering inequalities. Quantum Inf. Process. 18, 315 (2019)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  12. Branciard, C., Cavalcanti, E.G., Walborn, S.P., Scarani, V., Wiseman, H.M.: One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering. Phys. Rev. A 85, 010301 (2012)

    Article  ADS  Google Scholar 

  13. He, Q.Y., Rosales-Zárate, L., Adesso, G., Reid, M.D.: Secure continuous variable teleportation and Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 115, 180502 (2015)

    Article  ADS  Google Scholar 

  14. Cheng, W.W., Wang, B.W., Gong, L.Y., Zhao, S.M.: Dynamics of Einstein–Podolsky–Rosen steering in Heisenberg model under decoherence. Quantum Inf. Process. 20, 371 (2021)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  15. Li, C.-M., Chen, K., Chen, Y.-N., Zhang, Q., Chen, Y.-A., Pan, J.-W.: Genuine high-order Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 115, 010402 (2015)

    Article  ADS  Google Scholar 

  16. Chen, Y.-N., Li, C.-M., Lambert, N., Chen, S.-L., Ota, Y., Chen, G.-Y., Nori, F.: Temporal steering inequality. Phys. Rev. A 89, 032112 (2014)

    Article  ADS  Google Scholar 

  17. Chen, S.-L., Lambert, N., Li, C.-M., Miranowicz, A., Chen, Y.-N., Nori, F.: Quantifying non-Markovianity with temporal steering. Phys. Rev. Lett. 116, 020503 (2016)

    Article  ADS  Google Scholar 

  18. Bartkiewicz, K., Černoch, A., Lemr, K., Miranowicz, A., Nori, F.: Temporal steering and security of quantum key distribution with mutually unbiased bases against individual attacks. Phys. Rev. A 93, 062345 (2016)

    Article  ADS  Google Scholar 

  19. Ku, H.-Y., Chen, S.-L., Chen, H.-B., Lambert, N., Chen, Y.-N., Nori, F.: Temporal steering in four dimensions with applications to coupled qubits and magnetoreception. Phys. Rev. A 94, 062126 (2016)

    Article  ADS  Google Scholar 

  20. Liu, B., Huang, Y., Sun, Z.: Quantum temporal steering in a dephasing channel with quantum criticality. Ann. Phys. (Berlin) 530, 1700373 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  21. Cheng, W.W., Chen, M., Gong, L.Y., Zhao, S.M.: Quantum temporal steering in a noise channel with topological characterization. Eur. Phys. J. D 75, 75 (2021)

    Article  ADS  Google Scholar 

  22. Ban, M.: Temporal steering of a two-level system interacting with a coherent superposition of two environments. Quantum Inf. Process. 21, 13 (2022)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  23. Martens, C.C.: Quantum dephasing of a two-state system by a nonequilibrium harmonic oscillator. J. Chem. Phys. 139, 024109 (2013)

    Article  ADS  Google Scholar 

  24. Lombardo, F.C., Villar, P.I.: A Nonunitary geometric phases: a qubit coupled to an environment with random noise. Phys. Rev. A 87, 032338 (2013)

    Article  ADS  Google Scholar 

  25. Schiró, M., Mitra, A.: Transient orthogonality catastrophe in a time-dependent nonequilibrium environment. Phys. Rev. Lett. 112, 246401 (2014)

    Article  ADS  Google Scholar 

  26. Peronaci, F., Schiró, M., Capone, M.: Transient dynamics of d-wave superconductors after a sudden excitation. Phys. Rev. Lett. 115, 257001 (2015)

    Article  ADS  Google Scholar 

  27. Fuliński, A.: Non-Markovian noise. Phys. Rev. E 50, 2668 (1994)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  28. Cai, X., Zheng, Y.: Decoherence induced by non-Markovian noise in a nonequilibrium environment. Phys. Rev. A 94, 042110 (2016)

    Article  ADS  Google Scholar 

  29. Cai, X., Zheng, Y.: Non-Markovian decoherence dynamics in nonequilibrium environments. J. Chem. Phys. 149, 094107 (2018)

    Article  ADS  Google Scholar 

  30. Cai, X., Zheng, Y.: Quantum dynamical speedup in a nonequilibrium environment. Phys. Rev. A 95, 052104 (2017)

    Article  ADS  Google Scholar 

  31. Lin, D., Zou, H.M., Yang, J.: Based-nonequilibrium-environment non-Markovianity, quantum Fisher information and quantum coherence. Phys. Scr. 95, 015103 (2020)

    Article  ADS  Google Scholar 

  32. Cai, X., Meng, R., Zhang, Y., Wang, L.: Geometry of quantum evolution in a nonequilibrium environment. EPL 125, 30007 (2019)

    Article  ADS  Google Scholar 

  33. Chen, M., Chen, H., Han, T., Cai, X.: Disentanglement dynamics in nonequilibrium environments. Entropy 24, 1330 (2022)

    Article  MathSciNet  ADS  Google Scholar 

  34. Basit, A., Ali, H., Badshah, F., Yang, X.-F., Ge, G.Q.: Nonequilibrium effects on one-norm geometric correlations and the emergence of a pointer-state basis in the weak- and strong-coupling regimes. Phys. Rev. A 104, 042417 (2021)

    Article  ADS  Google Scholar 

  35. Basit, A., Ali, H., Badshah, F., Yang, X.-F., Ge, G.Q.: Controlling sudden transition from classical to quantum decoherence via non-equilibrium environments. New J. Phys. 22, 033039 (2020)

    Article  ADS  Google Scholar 

  36. Breuer, H.-P., Laine, E.-M., Piilo, J.: Measure for the degree of non-Markovian behavior of quantum processes in open systems. Phys. Rev. Lett. 103, 210401 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  37. Rivas, A., Huelga, S.F., Plenio, M.B.: Entanglement and non-Markovianity of quantum evolutions. Phys. Rev. Lett. 105, 050403 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  38. Luo, S., Fu, S., Song, H.: Quantifying non-Markovianity via correlations. Phys. Rev. A 86, 044101 (2012)

    Article  ADS  Google Scholar 

  39. Mazzola, L., Laine, E.-M., Breuer, H.-P., Maniscalco, S., Piilo, J.: Phenomenological memory-kernel master equations and time-dependent Markovian processes. Phys. Rev. A 81, 062120 (2010)

    Article  ADS  Google Scholar 

  40. Xu, Z.-Y., Luo, S., Yang, W.L., Liu, C., Zhu, S.Q.: Quantum speedup in a memory environment. Phys. Rev. A 89, 012307 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank the support from the Natural Science Foundation of Nanjing University of Posts and Telecommunication (Grant No. NY218005) and the Natural Science Foundation of China (Grant No. 61871234).

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  1. Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China

    W. W. Cheng & B. Li

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  1. W. W. Cheng
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Cheng, W.W., Li, B. Nonequilibrium effects on quantum temporal steering. Quantum Inf Process 22, 294 (2023). https://doi.org/10.1007/s11128-023-04053-7

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