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Average measurement-dependent symmetric discord

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Abstract

The measurement-dependent symmetric quantum discord is defined as the measurement-induced disturbance, where the given local von Neumann measurement is performed locally on both subsystems. For general bipartite quantum systems, we investigate the average measurement-dependent symmetric quantum discord. It can be considered as an upper bound of the symmetric quantum discord and the difference between them can be considered as the evaluation error as a result of the lack of prior information. Firstly, we derive a product measure on the unitary group \(\mathrm {U}(d_{A})\otimes \mathrm {U}(d_{B})/\sim \) induced by the uniform Haar measure over the unitary group \(\mathrm {U}(d)\). Then applying this measure, we analyze integrals related to the measurement-dependent symmetric quantum discord over the unitary group and obtain analytic expressions for the average measurement-dependent symmetric quantum discord after parameterization. The expressions allow us to calculate the symmetric quantum discord in an average sense with relatively few parameters.

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Data availability

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work is supported by Key Research and Development Project of Guangdong Province under Grant No. 2020B0303300001 and the Guangdong Basic and Applied Basic Research Foundation under Grant No. 2020B1515310016.

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Authors and Affiliations

  1. Department of Mathematics, South China University of Technology, Guangzhou, 510640, People’s Republic of China

    Jin-Wei Huang & Zhu-Jun Zheng

  2. Laboratory of Quantum Science and Engineering, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Jin-Wei Huang & Zhu-Jun Zheng

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  1. Jin-Wei Huang
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  2. Zhu-Jun Zheng
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Correspondence to Zhu-Jun Zheng.

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Huang, JW., Zheng, ZJ. Average measurement-dependent symmetric discord. Quantum Inf Process 21, 247 (2022). https://doi.org/10.1007/s11128-022-03599-2

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