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The Measurement-Disturbance Relation and the Disturbance Trade-off Relation in Terms of Relative Entropy

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Abstract

We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the measurement-disturbance relation and the disturbance trade-off relation. We find that without quantum memory the disturbance induced by the measurement is never less than the measurement uncertainty and with quantum memory they depend on the conditional entropy of the measured state. We also generalize these relations to the case with multiple measurements. These relations are demonstrated by two examples.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China, under Grant No.11375036, the Xinghai Scholar Cultivation Plan and the Fundamental Research Funds for the Central Universities under Grants No. DUT15LK35 and No. DUT15TD47.

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Authors and Affiliations

  1. School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian, 116024, China

    Jun Zhang, Yang Zhang & Chang-shui Yu

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  1. Jun Zhang
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  2. Yang Zhang
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  3. Chang-shui Yu
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Correspondence to Chang-shui Yu.

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Zhang, J., Zhang, Y. & Yu, Cs. The Measurement-Disturbance Relation and the Disturbance Trade-off Relation in Terms of Relative Entropy. Int J Theor Phys 55, 3943–3953 (2016). https://doi.org/10.1007/s10773-016-3024-9

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  • DOI: https://doi.org/10.1007/s10773-016-3024-9

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