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Rényi entropy uncertainty relation for successive projective measurements

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Abstract

We investigate the uncertainty principle for two successive projective measurements in terms of Rényi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty relations with a lower optimal bound. We compare our relation with other formulations of the uncertainty principle in two-spin observables measured on a pure quantum state of qubit. It is shown that the low bound of our uncertainty relation has better tightness.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China, under Grants numbers 11375036 and 11175033, and the Xinghai Scholar Cultivation Plan.

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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. Rényi entropy uncertainty relation for successive projective measurements. Quantum Inf Process 14, 2239–2253 (2015). https://doi.org/10.1007/s11128-015-0950-z

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