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Controlling quantum memory-assisted entropic uncertainty in non-Markovian environments

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Abstract

Quantum memory-assisted entropic uncertainty relation (QMA EUR) addresses that the lower bound of Maassen and Uffink’s entropic uncertainty relation (without quantum memory) can be broken. In this paper, we investigated the dynamical features of QMA EUR in the Markovian and non-Markovian dissipative environments. It is found that dynamical process of QMA EUR is oscillation in non-Markovian environment, and the strong interaction is favorable for suppressing the amount of entropic uncertainty. Furthermore, we presented two schemes by means of prior weak measurement and posterior weak measurement reversal to control the amount of entropic uncertainty of Pauli observables in dissipative environments. The numerical results show that the prior weak measurement can effectively reduce the wave peak values of the QMA-EUA dynamic process in non-Markovian environment for long periods of time, but it is ineffectual on the wave minima of dynamic process. However, the posterior weak measurement reversal has an opposite effects on the dynamic process. Moreover, the success probability entirely depends on the quantum measurement strength. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.

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References

  1. Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Physics 43, 172–198 (1927)

    Article  MATH  Google Scholar 

  2. Robertson, H.P.: The uncertainty principle. Phys. Rev. 34, 163 (1929)

    Article  ADS  Google Scholar 

  3. Maassen, H., Uffink, J.B.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  4. Renes, J.M., Boilean, J.C.: Conjectured strong complementary information tradeoff. Phys. Rev. Lett. 103, 020402 (2009)

    Article  ADS  Google Scholar 

  5. Berta, M., Christand, M., Colbeck, R., Renes, J.M., Benner, B.: The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659–662 (2010)

    Article  Google Scholar 

  6. Dressel, J., Nori, F.: Certainty in Heisenberg’s uncertainty principle: revisiting definitions for estimation errors and disturbance. Phys. Rev. A 89, 022106 (2014)

    Article  ADS  Google Scholar 

  7. Xu, Z.Y., Zhu, S.Q., Yang, W.L.: Quantum-memory-assisted entropic uncertainty relation with a single nitrogen-vacancy center in diamond. Appl. Phys. Lett. 101, 244105 (2012)

    Article  ADS  Google Scholar 

  8. Prevedel, R., Hamel, D.R., Colbeck, R., Fisher, K., Resch, K.J.: Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement. Nat. Phys. 7, 757–761 (2011)

    Article  Google Scholar 

  9. Li, C.F., Xu, J.S., Xu, X.Y., Li, K., Guo, G.C.: Experimental investigation of the entanglement-assisted entropic uncertainty principle. Nat. Phys. 7, 752–756 (2011)

    Article  Google Scholar 

  10. Xiang, Z.L., Ashhab, S., You, J.Q., Nori, F.: Hybrid quantum circuits: superconducting circuits interacting with other quantum systems. Rev. Mod. Phys. 85, 623 (2013)

    Article  ADS  Google Scholar 

  11. Adabi, F., Salimi, S., Haseli, S.: Tightening the entropic uncertainty bound in the presence of quantum memory. Phys. Rev. A 93, 062123 (2016)

    Article  ADS  Google Scholar 

  12. Pati, A.K., Wilde, M.M., Devi, A.R.U., et al.: Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory. Phys. Rev. A 86, 042105 (2012)

    Article  ADS  Google Scholar 

  13. Ma, J., Sun, Z., Wang, X.G., Nori, F.: Entanglement dynamics of two qubits in a common bath. Phys. Rev. A 85, 062323 (2012)

    Article  ADS  Google Scholar 

  14. You, J.Q., Hu, X., Nori, F.: Correlation-induced suppression of decoherence in capacitively coupled cooper-pair boxes. Phys. Rev. B 72, 144529 (2005)

    Article  ADS  Google Scholar 

  15. Xu, Z.Y., Yang, W.L., Feng, M.: Quantum-memory-assisted entropic uncertainty relation under noise. Phys. Rev. A 86, 012113 (2012)

    Article  ADS  Google Scholar 

  16. Hu, M., Fan, H.: Quantum-memory-assisted entropic uncertainty principle, teleportation, and entanglement witness in structured reservoirs. Phys. Rev. A 86, 032338 (2012)

    Article  ADS  Google Scholar 

  17. Yao, C.M., Chen, Z.H., Ma, Z.H., Severini, S., Serafini, A.: A Entanglement and discord assisted entropic uncertainty relations under decoherence. Sci China Phys Mech Astron 57, 1703–1711 (2014)

    Article  ADS  Google Scholar 

  18. Zou, H.M., Fang, M.F., Yang, B.Y., Guo, Y.N., He, W., Zhang, S.Y.: The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments. Phys. Scr. 89, 115101 (2014)

    Article  ADS  Google Scholar 

  19. Kofman, A.G., Ashhab, S., Nori, F.: Nonperturbative theory of weak pre- and post-selected measurements. Phys. Rep. 520, 43–133 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  20. Ota, Y., Ashhab, S., Nori, F.: Entanglement amplification via local weak measurements. J. Phys. A Math. Theor. 45, 415303 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Dressel, J., Bliokh, K.Y., Nori, F.: Classical field approach to quantum weak measurements. Phys. Rev. Lett. 112, 110407 (2014)

    Article  ADS  Google Scholar 

  22. Bliokh, K.Y., Bekshaev, A.Y., Kofman, A.G., Nori, F.: Photon trajectories, anomalous velocities, and weak measurements: a classical interpretation. New J. Phys. 15, 73022–73038 (2013)

    Article  Google Scholar 

  23. Zhou, L., Turek, Y., Sun, C.P., Nori, F.: Weak-value amplification of light deflection by a dark atomic ensemble. Phys. Rev. A 88, 053815 (2013)

    Article  ADS  Google Scholar 

  24. Xiao, X., Feng, M.: Reexamination of the feedback control on quantum states via weak measurements. Phys. Rev. A 83, 054301 (2011)

    Article  ADS  Google Scholar 

  25. Zhang, Y.J., Han, W., Fan, H., Xia, Y.J.: Enhancing entanglement trapping by weak measurement and quantum measurement reversal. Ann. Phys. 354, 203–212 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Nourmandipour, A., Tavassoly, M.K., Rafiee, M.: Dynamics and protection of entanglement in n-qubit systems within Markovian and non-Markovian environments. Phys. Rev. A 93, 022327 (2016)

    Article  ADS  Google Scholar 

  27. Sun, Q., Al-Amri, M., Davidovich, L., Zubairy, M.S.: Reversing entanglement change by a weak measurement. Phys. Rev. A 82, 052323 (2010)

    Article  ADS  Google Scholar 

  28. He, Z., Yao, C.M., Zou, J.: Robust state transfer in the quantum spin channel via weak measurement and quantum measurement reversal. Phys. Rev. A 88, 044304 (2013)

    Article  ADS  Google Scholar 

  29. Zong, X.L., Du, C.Q., Yang, M., Yang, Q., Cao, Z.L.: Protecting remote bipartite entanglement against amplitude damping by local unitary operations. Phys. Rev. A 90, 062345 (2014)

    Article  ADS  Google Scholar 

  30. Liu, H.B., Yang, W.L., An, J.H., Xu, Z.Y.: Mechanism for quantum speedup in open quantum systems. Phys. Rev. A 93, 020105(R) (2016)

    Article  ADS  Google Scholar 

  31. Haseli, S., Karpat, G., Salimi, S., Khorashad, A.S., Fanchini, F.F., Cakmak, B., Aguilar, G.H., Walborn, S.P., Souto Ribeiro, P.H.: Non-Markovianity through flow of information between a system and an environment. Phys. Rev. A 90, 052118 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

Download references

Acknowledgements

The work was supported by the National Natural Science Foundation of China under Grant Nos. 11374096 and 11464015, the Natural Science Foundation of Hunan Province under Grant No. 14jj6035, the Science Research Foundation of Education Department of Hunan Province under Grant No. 14B147.

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Authors and Affiliations

  1. Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Synergetic Innovation Center for Quantum Effects and Applications, College of Physics and Information Science, Hunan Normal University, Changsha, 410081, People’s Republic of China

    Yanliang Zhang & Maofa Fang

  2. School of Software and Service Outsourcing, Jishou University, Zhangjiajie, 427000, People’s Republic of China

    Yanliang Zhang, Guodong Kang & Qingping Zhou

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  1. Yanliang Zhang
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  2. Maofa Fang
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  3. Guodong Kang
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  4. Qingping Zhou
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Correspondence to Maofa Fang.

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Zhang, Y., Fang, M., Kang, G. et al. Controlling quantum memory-assisted entropic uncertainty in non-Markovian environments. Quantum Inf Process 17, 62 (2018). https://doi.org/10.1007/s11128-018-1822-0

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  • DOI: https://doi.org/10.1007/s11128-018-1822-0

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