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Decoherence effect on quantum-memory-assisted entropic uncertainty relations

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Abstract

Uncertainty principle significantly provides a bound to predict precision of measurement with regard to any two incompatible observables, and thereby plays a nontrivial role in quantum precision measurement. In this work, we observe the dynamical features of the quantum-memory-assisted entropic uncertainty relations (EUR) for a pair of incompatible measurements in an open system characterized by local generalized amplitude damping (GAD) noises. Herein, we derive the dynamical evolution of the entropic uncertainty with respect to the measurement affecting by the canonical GAD noises when particle A is initially entangled with quantum memory B. Specifically, we examine the dynamics of EUR in the frame of three realistic scenarios: one case is that particle A is affected by environmental noise (GAD) while particle B as quantum memory is free from any noises, another case is that particle B is affected by the external noise while particle A is not, and the last case is that both of the particles suffer from the noises. By analytical methods, it turns out that the uncertainty is not full dependent of quantum correlation evolution of the composite system consisting of A and B, but the minimal conditional entropy of the measured subsystem. Furthermore, we present a possible physical interpretation for the behavior of the uncertainty evolution by means of the mixedness of the observed system; we argue that the uncertainty might be dramatically correlated with the systematic mixedness. Furthermore, we put forward a simple and effective strategy to reduce the measuring uncertainty of interest upon quantum partially collapsed measurement. Therefore, our explorations might offer an insight into the dynamics of the entropic uncertainty relation in a realistic system, and be of importance to quantum precision measurement during quantum information processing.

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References

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

    Article  ADS  MATH  Google Scholar 

  2. Robertson, H.P.: Violation of Heisenberg’s uncertainty principle. Phys. Rev. 34, 163 (1929)

    Article  ADS  Google Scholar 

  3. Kennard, E.H.: Zur Quantenmechanik einfacher Bewegungstypen. Z. Phys. 44, 326 (1927)

    Article  ADS  MATH  Google Scholar 

  4. Deutsch, D.: Uncertainty in quantum measurements. Phys. Rev. Lett. 50, 631–633 (1983)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  7. Berta, M., Christandl, M., Colbeck, R., Renes, J.M., Renner, R.: The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659–662 (2010)

    Article  Google Scholar 

  8. Renes, J.M., Boileau, J.C.: Physical underpinnings of privacy. Phys. Rev. A 78, 032335 (2008)

    Article  ADS  Google Scholar 

  9. Wild, M.M., Renes, J.M.: In: Proceeding of International Symposium on Information Theory. IEEE, Cambridge, Masschusetts, pp. 334–338 (2012)

  10. Kim, Y.H., Shih, Y.: Experimental realization of popper’s experiment: violation of the uncertainty principle? Found. Phys. 29, 1849 (1999)

    Article  Google Scholar 

  11. Tomamichel, M., Renner, R.: Uncertainty relation for smooth entropies. Phys. Rev. Lett. 106, 110506 (2011)

    Article  ADS  Google Scholar 

  12. 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 

  13. Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  14. Coles, P.J., Colbeck, R., Yu, L., Zwolak, M.: Uncertainty relations from simple entropic properties. Phys. Rev. Lett. 108, 210405 (2012)

    Article  ADS  Google Scholar 

  15. 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 

  16. 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 

  17. 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 

  18. Pati, A.K., 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 

  19. Pramanik, T., Mal, S., Majumdar, A.S.: Lower bound of quantum uncertainty from extractable classical information. Quantum Inf. Process. 15, 981–999 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Wang, K.K., Zhan, X., Bian, Z.H., Li, J., Zhang, Y.S., Xue, P.: Experimental investigation of the stronger uncertainty relations for all incompatible observables. Phys. Rev. A 93, 052108 (2016)

    Article  ADS  Google Scholar 

  21. Hu, M.L., Fan, H.: Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation. Phys. Rev. A 87, 022314 (2013)

    Article  ADS  Google Scholar 

  22. Hu, M.L., Fan, H.: Upper bound and shareability of quantum discord based on entropic uncertainty relations. Phys. Rev. A 88, 014105 (2013)

    Article  ADS  Google Scholar 

  23. Sun, Y.H., Kuang, L.M.: Quantum decoherence for multi-photon entangled states. Chin. Phys. Lett. 22, 1833–1836 (2005)

    Article  ADS  Google Scholar 

  24. Sun, W.Y., Wang, D., Shi, J.D., Ye, L.: Exploration quantum steering, nonlocality and entanglement of two-qubit X-state in structured reservoirs. Sci. Rep. 7, 39651 (2017)

    Article  ADS  Google Scholar 

  25. Sun, W.Y., Wang, D., Yang, J., Ye, L.: Enhancement of multipartite entanglement in an open system under non-inertial frames. Quantum Inf. Process. 16, 90 (2017)

    Article  ADS  MATH  Google Scholar 

  26. 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 

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

    Article  ADS  Google Scholar 

  28. Zhang, Y.L., Fang, M.F., Kang, G.D., Zhou, Q.P.: Reducing quantum-memory-assisted entropic uncertainty by weak measurement and weak measurement reversal. Int. J. Quantum Inf. 13, 1550037 (2015)

    Article  MATH  Google Scholar 

  29. 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 

  30. Hu, Y.D., Zhang, S.B., Wang, D., Ye, L.: Entropic uncertainty relation under dissipative environments and its steering by local non-unitary operations. Int. J. Theor. Phys. 55, 4641–4650 (2016)

    Article  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. Horodecki, R., Horodecki, M.: Information-theoretic aspects of inseparability of mixed states. Phys. Rev. A 54, 1838 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  MATH  Google Scholar 

  34. Hu, M.L., Hu, X.Y., Wang, J.C., Peng, Y., Zhang, Y.R., Fan, H.: Quantum coherence and quantum correlations. arXiv:1703.01852 (2017)

  35. Hu, M.L.: Disentanglement, Bell-nonlocality violation and teleportation capacity of the decaying tripartite states. Ann. Phys. 327, 2332–2342 (2012)

    Article  ADS  MATH  Google Scholar 

  36. Christopher, K., Mary, B.R.: Minimal entropy of states emerging from noisy quantum channels. IEEE Trans. Inf. Theory 47, 192 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  37. Peters, N.A., Wei, T.C., Kwiat, P.G.: Mixed-state sensitivity of several quantum-information benchmarks. Phys. Rev. A 70, 052309 (2004)

    Article  ADS  Google Scholar 

  38. Singh, U., Bera, M.N., Dhar, H.S., Pati, A.K.: Maximally coherent mixed states: complementarity between maximal coherence and mixedness. Phys. Rev. A 91, 052115 (2015)

    Article  ADS  Google Scholar 

  39. Korotkov, A.N., Jordan, A.N.: Undoing a weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)

    Article  ADS  Google Scholar 

  40. Wang, S.C., Yu, Z.W., Zou, W.J., Wang, X.B.: Protecting quantum states from decoherence of finite temperature using weak measurement. Phys. Rev. A 89, 022318 (2014)

    Article  ADS  Google Scholar 

  41. 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  Google Scholar 

  42. 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 

Download references

Acknowledgements

This work was supported by the National Science Foundation of China under Grant Nos. 61601002 and 11575001, Anhui Provincial Natural Science Foundation (Grant No. 1508085QF139), and the fund from CAS Key Laboratory of Quantum Information (Grant No. KQI201701).

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Authors and Affiliations

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

    Fei Ming, Dong Wang, Ai-Jun Huang, Wen-Yang Sun & Liu Ye

  2. CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China

    Dong Wang

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  1. Fei Ming
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  2. Dong Wang
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  3. Ai-Jun Huang
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  4. Wen-Yang Sun
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Correspondence to Dong Wang.

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Ming, F., Wang, D., Huang, AJ. et al. Decoherence effect on quantum-memory-assisted entropic uncertainty relations. Quantum Inf Process 17, 9 (2018). https://doi.org/10.1007/s11128-017-1785-6

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  • DOI: https://doi.org/10.1007/s11128-017-1785-6

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