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Quantum-memory-assisted entropic uncertainty relations under weak measurements

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Abstract

We investigate quantum-memory-assisted entropic uncertainty relations (EURs) based on weak measurements. It is shown that the lower bound of EUR revealed by weak measurements is always larger than that revealed by the corresponding projective measurements. A series of lower bounds of EUR under both weak measurements and projective measurements are presented. Interestingly, the quantum-memory-assisted EUR based on weak measurements is a monotonically decreasing function of the strength parameter. Furthermore, some information-theoretic inequalities associated with weak measurements are also derived.

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Acknowledgements

This research was supported by the grants from the Natural Science Foundation of China (11571220) and (11105226); the Natrual Science Foundation of Shandong Province (ZR2016AM23); the Fundamental Research Funds for the Central Universities Nos. (15CX02075A) and (15CX05062A); Macao Science and Technology Development Fund No. (003/2015/A1).

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Lei Li & Qing-Wen Wang

  2. College of Science, China University of Petroleum, Qingdao, 266580, People’s Republic of China

    Lei Li, Shu-Qian Shen & Ming Li

Authors
  1. Lei Li
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  2. Qing-Wen Wang
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  3. Shu-Qian Shen
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  4. Ming Li
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Correspondence to Qing-Wen Wang.

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Li, L., Wang, QW., Shen, SQ. et al. Quantum-memory-assisted entropic uncertainty relations under weak measurements. Quantum Inf Process 16, 188 (2017). https://doi.org/10.1007/s11128-017-1638-3

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