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Exploring maximal steered coherence and entanglement via quantum steering ellipsoid framework

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Abstract

All two-qubit states can be characterized visually by a quantum steering ellipsoid (QSE) inside the Bloch sphere, and their quantum resources (such as entanglement and discord) can be directly reflected via the geometric properties of QSE. In this work, we obtain QSE of bipartite Werner state interacting with a reservoir and probe the effects of the strong coupling regime and weak coupling regime on the maximal steered coherence (MSC) and concurrence in QSE framework. It is concluded that the MSC can be identified by the length of x or y semiaxis of ellipsoid. Meanwhile, the concurrence is related to the lengths of x and z semiaxes of QSE. The information can flow bidirectionally between the qubit system and the non-Markovian environment, which can induce the shrink, inflation and movement of ellipsoid in the Bloch sphere. On the contrary, due to the decoherence of information within Markovian environment, the QSE gradually shrinks and then eventually disappears in the north pole of Bloch sphere. Therefore, the evolutions of MSC and concurrence can be mapped by the aforementioned dynamics of QSE. The results also reveal that MSC and concurrence can be enhanced by suppressing the degradation of ellipsoid’s semiaxis. Moreover, we investigate the inflation of QSE under filtering operation and derive the condition of increasing MSC. An optimal operation strength of filtering operation is also obtained. It is worth noting that MSC and concurrence can be frozen by the optimal strength in the strong coupling and weak coupling regimes.

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References

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

    Article  ADS  Google Scholar 

  2. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  3. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  4. Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  7. Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493 (1995)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Asbóth, J.K., Calsamiglia, J., Ritsch, H.: Computable measure of nonclassicality for light. Phys. Rev. Lett. 94, 173602 (2005)

    Article  ADS  Google Scholar 

  10. Matera, J.M., Egloff, D., Killoran, N., Plenio, M.B.: Coherent control of quantum systems as a resource theory. Quantum Sci. Technol. 1, 01LT01 (2016)

    Article  Google Scholar 

  11. Ma, J.J., Yadin, B., Girolami, D., Vedral, V., Gu, M.: Converting coherence to quantum correlations. Phys. Rev. Lett. 116, 160407 (2016)

    Article  ADS  Google Scholar 

  12. Hillery, M.: Coherence as a resource in decision problems: the Deutsch–Jozsa algorithm and a variation. Phys. Rev. A 93, 012111 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Uhlmann, A.: Fidelity and concurrence of conjugated states. Phys. Rev. A 62, 032307 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  15. Rungta, P., Bužek, V., Caves, C.M., Hillery, M., Milburn, G.J.: Universal state inversion and concurrence in arbitrary dimensions. Phys. Rev. A 64, 042315 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  16. Carvalho, A.R.R., Mintert, F., Buchleitner, A.: Decoherence and multipartite entanglement. Phys. Rev. Lett. 93, 230501 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Schrödinger, E.: Discussion of probability relations between separated systems. Math. Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  ADS  Google Scholar 

  20. Quintino, M.T., Brunner, N.: Superactivation of quantum steering. Phys. Rev. A 94, 062123 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  22. Cavalcanti, D., Skrzypczyk, P., Aguilar, G.H., Nery, R.V., Ribeiro, P.H.S., Walborn, S.P.: Detection of entanglement in asymmetric quantum networks and multipartite quantum steering. Nat. Commun. 6, 7941 (2015)

    Article  ADS  Google Scholar 

  23. Armstrong, S., Wang, M., Teh, R.Y., Gong, Q.H., He, Q.Y., Janousele, J., Bachor, H.A., Reid, M.D., Lam, P.K.: Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks. Nat. Phys. 11, 167 (2015)

    Article  Google Scholar 

  24. 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 

  25. 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 

  26. Rutkowski, A., Buraczewski, A., Horodecki, P., Stobińska, M.: Quantum steering inequality with tolerance for measurement-setting errors: experimentally feasible signature of unbounded violation. Phys. Rev. Lett. 118, 020402 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  27. Kaur, E., Wang, X.T., Wilde, M.M.: Conditional mutual information and quantum steering. Phys. Rev. A 96, 022332 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  28. Jevtic, S., Pusey, M., Jennings, D., Rudolph, T.: Quantum steering ellipsoids. Phys. Rev. Lett. 113, 020402 (2014)

    Article  ADS  Google Scholar 

  29. Milne, A., Jevtic, S., Jennings, D., Wiseman, H., Rudolph, T.: Quantum steering ellipsoids, extremal physical states and monogamy. New J. Phys. 16, 083017 (2014)

    Article  ADS  Google Scholar 

  30. Milne, A., Jennings, D., Jevtic, S., Rudolph, T.: Quantum correlations of two-qubit states with one maximally mixed marginal. Phys. Rev. A 90, 024302 (2014)

    Article  ADS  Google Scholar 

  31. Shi, M.J., Jiang, F.J., Sun, C.X., Du, J.F.: Geometric picture of quantum discord for two-qubit quantum states. New J. Phys. 13, 073016 (2011)

    Article  ADS  Google Scholar 

  32. Shi, M.J., Sun, C.X., Jiang, F.J., Yan, X.H., Du, J.F.: Optimal measurement for quantum discord of two-qubit states. Phys. Rev. A 85, 064104 (2012)

    Article  ADS  Google Scholar 

  33. Nguyen, H.C., Vu, T.: Nonseparability and steerability of two-qubit states from the geometry of steering outcomes. Phys. Rev. A 94, 012114 (2016)

    Article  ADS  Google Scholar 

  34. Jevtic, S., Hall, M.J.W., Anderson, M.R., Zwierz, M., Wiseman, H.M.: Einstein–Podolsky–Rosen steering and the steering ellipsoid. J. Opt. Soc. Am. B 32, A40 (2015)

    Article  ADS  Google Scholar 

  35. Quan, Q., Zhu, H.J., Liu, S.Y., Fei, S.M., Fan, H., Yang, W.L.: Steering Bell-diagonal states. Sci. Rep. 6, 22025 (2016)

    Article  ADS  Google Scholar 

  36. Nguyen, H.C., Vu, T.: Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes. Europhys. Lett. 115, 10003 (2016)

    Article  Google Scholar 

  37. McCloskey, R., Ferraro, A., Paternostro, M.: Einstein–Podolsky–Rosen steering and quantum steering ellipsoids: optimal two-qubit states and projective measurements. Phys. Rev. A 95, 012320 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  38. Caban, P., Rembielinski, J., Smolinski, K.A., Walczak, Z.: SLOCC orbit of rank-deficient two-qubit states: quantum entanglement, quantum discord and EPR. Quantum Inf. Process. 16, 178 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  39. Hu, X.Y., Milne, A., Zhang, B.Y., Fan, H.: Quantum coherence of steered states. Sci. Rep. 6, 19365 (2016)

    Article  ADS  Google Scholar 

  40. Cheng, J., Zhang, W.Z., Han, Y., Zhou, L.: Robust fermionic-mode entanglement of a nanoelectronic system in non-Markovian environments. Phys. Rev. A 91, 022328 (2015)

    Article  ADS  Google Scholar 

  41. Altintas, F., Eryigit, R.: Quantum correlations in non-Markovian environments. Phys. Lett. A 374, 4283 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  42. Wang, D., Huang, A.J., Hoehn, R.D., Ming, F., Sun, W.Y., Shi, J.D., Ye, L., Kais, S.: Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir. Sci. Rep. 7, 1066 (2017)

    Article  ADS  Google Scholar 

  43. Bellomo, B., Franco, R.L., Compagno, G.: Non-Markovian effects on the dynamics of entanglement. Phys. Rev. Lett. 99, 160502 (2007)

    Article  ADS  Google Scholar 

  44. Dhar, H.S., Bera, M.N., Adesso, G.: Characterizing non-Markovianity via quantum interferometric power. Phys. Rev. A 91, 032115 (2015)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  46. Maniscalco, S., Petruccione, F.: Non-Markovian dynamics of a qubit. Phys. Rev. A 73, 012111 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  47. 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 

  48. Hu, X.Y., Fan, H.: Effect of local channels on quantum steering ellipsoids. Phys. Rev. A 91, 022301 (2015)

    Article  ADS  Google Scholar 

  49. 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 

  50. Bromley, T.R., Cianciaruso, M., Adesso, G.: Frozen quantum coherence. Phys. Rev. Lett. 114, 210401 (2015)

    Article  ADS  Google Scholar 

  51. Yu, X.D., Zhang, D.J., Liu, C.L., Tong, D.M.: Measure-independent freezing of quantum coherence. Phys. Rev. A 93, 060303 (2016)

    Article  ADS  Google Scholar 

  52. Du, M.M., Wang, D., Ye, L.: How Unruh effect affects freezing coherence in decoherence. Quantum Inf. Process. 16, 228 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  53. Gisin, N.: Hidden quantum nonlocality revealed by local filters. Phys. Lett. A 210, 151156 (1996)

    MathSciNet  MATH  Google Scholar 

  54. Siomau, M., Kamli, A.A.: Defeating entanglement sudden death by a single local filtering. Phys. Rev. A 86, 032304 (2012)

    Article  ADS  Google Scholar 

  55. Karmakar, S., Sen, A., Bhar, A., Sarkar, D.: Effect of local filtering on freezing phenomena of quantum correlation. Quantum Inf. Process. 14, 2517 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Foundation of China under Grants Nos. 11575001 and 61601002, the Program for Excellent Talents in University of Anhui Province of China (Grant No. gxyq2018059), Anhui Provincial Natural Science Foundation (Grant No. 1508085QF139), the Key project of Anhui Provincial Department of Education (Grant Nos. KJ2017A406, KJ2017A401) and the Key Project of West Anhui University (Grant No. KJ103762015B23).

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Authors and Affiliations

  1. Institutes of Physical Science and Information Technology, Anhui University, Hefei, 230601, China

    Huan Yang, Chang-Jin Zhang & Liu Ye

  2. School of Physics and Material Science, Anhui University, Hefei, 230601, China

    Huan Yang, Zhi-Yong Ding, Wen-Yang Sun, Fei Ming, Xiao-Gang Fan, Dong Wang & Liu Ye

  3. Department of Experiment and Practical Training Management, West Anhui University, Lu’an, 237012, China

    Huan Yang

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Yang, H., Ding, ZY., Sun, WY. et al. Exploring maximal steered coherence and entanglement via quantum steering ellipsoid framework. Quantum Inf Process 18, 299 (2019). https://doi.org/10.1007/s11128-019-2414-3

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