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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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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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