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Controlling the quantum-memory-assisted entropic uncertainty relation by quantum-jump-based feedback control in dissipative environments

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Abstract

The dynamic properties of the quantum-memory-assisted entropic uncertainty relation for a system comprised of a qubit to be measured and a memory qubit are investigated. We explore the behaviors of the entropic uncertainty and its lower bound in three different cases: Only one of the two qubits interacts with an external environment and subjects to quantum-jump-based feedback control, or both of the two qubits independently experience their own environments and local quantum-jump-based feedback control. Our results reveal that the quantum-jump-based feedback control with an appropriate feedback parameter can reduce the entropic uncertainty and its lower bound, and for the three different scenarios, the reduction in the uncertainty relates to different physical quantities. Besides, we find out that the quantum-jump-based feedback control not only can remarkably decrease the entropic uncertainty, but also can make the uncertainty reach its lower bound where the dynamical map becomes unital.

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References

  1. Heisenberg, W.: Überden anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172 (1927)

    Article  ADS  MATH  Google Scholar 

  2. Deutsch, D.: Uncertainty in quantum measurements. Phys. Rev. Lett. 50, 631 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  3. Kraus, K.: Complementary observables and uncertainty relations. Phys. Rev. D 35, 3070 (1987)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Berta, M., Christandl, M., Colbeck, R., Renes, J.M., Renner, R.: The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659 (2010)

    Article  Google Scholar 

  7. 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 (2011)

    Article  Google Scholar 

  8. 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 (2011)

    Article  Google Scholar 

  9. 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 

  10. Feng, J., Zhang, Y.Z., Gould, M.D., Fan, H.: Entropic uncertainty relations under the relativistic motion. Phys. Lett. B 726, 527 (2013)

    Article  ADS  MATH  Google Scholar 

  11. Pramanik, T., Mal, S., Majumdar, A.S.: Lower bound of quantum uncertainty from extractable classical information. Quantum Inf. Process. 15, 981 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. 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 

  13. Wang, D., Ming, F., Huang, A.J., Sun, W.Y., Shi, J.D., Ye, L.: Exploration of quantum-memory-assisted entropic uncertainty relations in a noninertial frame. Laser Phys. Lett. 14, 055205 (2017)

    Article  ADS  Google Scholar 

  14. Wang, D., Huang, A.J., Ming, F., Sun, W.Y., Liu, H.P., Liu, C.C., Ye, L.: Quantum-memory-assisted entropic uncertainty relation in a Heisenberg XYZ chain with an inhomogeneous magnetic field. Laser Phys. Lett. 14, 065203 (2017)

    Article  ADS  Google Scholar 

  15. Karpat, G., Piilo, J., Maniscalco, S.: Controlling entropic uncertainty bound through memory effects. Eur. Phys. Lett. 111, 50006 (2015)

    Article  ADS  Google Scholar 

  16. Zhang, S.Y., Fang, M.F., Yu, M.: Controlling of entropic uncertainty in qubits system under the generalized amplitude damping channel via weak measurements. Int. J. Theor. Phys. 55, 1824–1832 (2016)

    Article  MATH  Google Scholar 

  17. Huang, A.J., Shi, J.D., Wang, D., Ye, L.: Steering quantum-memory-assisted entropic uncertainty under unital and nonunital noises via filtering operations. Quantum Inf. Process. 16, 46 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  18. Zhang, S.Y., Fang, M.F., Zhang, Y.L., Guo, Y.N., Zhao, Y.J., Tang, W.W.: Reduction of entropic uncertainty in entangled qubits system by local PT-symmetric operation. Chin. Phys. B 24, 090304 (2015)

    Article  ADS  Google Scholar 

  19. Wiseman, H.M., Milburn, G.J.: Quantum theory of optical feedback via homodyne detection. Phys. Rev. Lett. 70, 548–551 (1993)

    Article  ADS  Google Scholar 

  20. Wiseman, H.M.: Quantum theory of continuous feedback. Phys. Rev. A 49, 2133–2150 (1994)

    Article  ADS  Google Scholar 

  21. Wang, J., Wiseman, H.M., Milburn, G.J.: Dynamical creation of entanglement by homodyne-mediated feedback. Phys. Rev. A 71, 042309 (2005)

    Article  ADS  Google Scholar 

  22. Carvalho, A.R.R., Hope, J.J.: Stabilizing entanglement by quantum-jump-based feedback. Phys. Rev. A 76, 010301(R) (2007)

    Article  ADS  MathSciNet  Google Scholar 

  23. Li, J.G., Zou, J., Shao, B., Cai, J.F.: Steady atomic entanglement with different quantum feedbacks. Phys. Rev. A 77, 012339 (2008)

    Article  ADS  Google Scholar 

  24. Carvalho, A.R.R., Reid, A.J.S., Hope, J.J.: Controlling entanglement by direct quantum feedback. Phys. Rev. A 78, 012334 (2008)

    Article  ADS  Google Scholar 

  25. Viola, L., Lloyd, S.: Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733–2744 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  26. Katz, G., Ratner, M.A., Kosloff, R.: Decoherence control by tracking a Hamiltonian reference molecule. Phys. Rev. Lett. 98, 203006 (2007)

    Article  ADS  Google Scholar 

  27. Ganesan, N., Tarn, T.J.: Decoherence control in open quantum system via classical feedback. Phys. Rev. A 75, 032323 (2007)

    Article  ADS  Google Scholar 

  28. Zhang, J., Li, C., Wu, R., Tarn, T., Liu, X.: Maximal suppression of decoherence in Markovian quantum systems. J. Phys. A 38, 6587–6601 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Sun, H.Y., Shu, P.L., Li, C., Yi, X.X.: Feedback control on geometric phase in dissipative two-level systems. Phys. Rev. A 79, 022119 (2009)

    Article  ADS  Google Scholar 

  30. Zheng, Q., Ge, L., Yao, Y., Zhi, Q.J.: Enhancing parameter precision of optimal quantum estimation by direct quantum feedback. Phys. Rev. A 91, 033805 (2015)

    Article  ADS  Google Scholar 

  31. Shao, X.Q., Zheng, T.Y., Zhang, S.: Engineering steady three atom singlet state via quantum-jump-based feedback. Phys. Rev. A 85, 042308 (2012)

    Article  ADS  Google Scholar 

  32. Shao, X.Q., Wang, Z.H., Liu, H.D., Yi, X.X.: Dissipative preparation of a tripartite singlet state in coupled arrays of cavities via quantum feedback control. Phys. Rev. A 94, 032307 (2016)

    Article  ADS  Google Scholar 

  33. Sun, W.M., Su, S.L., Jin, Z., Liang, Y., Zhu, A.D., Wang, H.F., Zhang, S.: Dissipative preparation of three-atom entanglement state via quantum feedback control. J. Opt. Soc. Am. B 32, 1873–1880 (2015)

    Article  ADS  Google Scholar 

  34. Chen, L., Wang, H.F., Zhang, S.: Entanglement dynamics of three atoms under quantum-jump-based control. J. Opt. Soc. Am. B 30, 475–481 (2013)

    Article  ADS  Google Scholar 

  35. Yu, M., Fang, M.F.: Steady and optimal entropy squeezing of a two-level atom with quantum-jump-based feedback and classical driving in a dissipative cavity. Quantum Inf. Process. 15, 4175 (2016)

    Article  ADS  MATH  Google Scholar 

  36. Phoenix, S.J.D., Knight, P.L.: Fluctuations and entropy in models of quantum optical resonance. Ann. Phys. 186, 381–407 (1988)

    Article  ADS  MATH  Google Scholar 

  37. Boukobza, E., Tannor, D.J.: Entropy exchange and entanglement in the Jaynes–Cummings model. Phys. Rev. A 71, 063821 (2005)

    Article  ADS  Google Scholar 

  38. King, C., Ruskai, M.B.: Minimal entropy of states emerging from noisy quantum channels. IEEE Trans. Inf. Theory 47, 192 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11374096) and Hunan Provincial Innovation Foundation for Postgraduate (CX2017B177).

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Authors and Affiliations

  1. Department of Physics, Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, China

    Min Yu & Mao-Fa Fang

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  1. Min Yu
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  2. Mao-Fa Fang
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Correspondence to Mao-Fa Fang.

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Yu, M., Fang, MF. Controlling the quantum-memory-assisted entropic uncertainty relation by quantum-jump-based feedback control in dissipative environments. Quantum Inf Process 16, 213 (2017). https://doi.org/10.1007/s11128-017-1666-z

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