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Entanglement polygon inequalities for pure states in qudit systems

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Abstract

Entanglement is one of the important resources in many quantum tasks. And the issue of high-dimensional entangled systems is intriguing. Here we consider the entanglement distribution of higher-dimensional multipartite systems. Specifically, we show that the n-qudit pure states satisfy the entanglement polygon inequality (EPI) in terms of geometrical entanglement measure, then we offer an entanglement indicator for three-qubit pure states based on the geometrical entanglement measure. At last, we show that the EPI is not generally valid for pure states in higher-dimensional systems in terms of negativity. Nevertheless, the above inequality is valid for higher-dimensional systems in terms of concurrence.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

X. S. was supported by the Fundamental Research Funds for the Central Universities (Grant No. ZY2306), and Funds of College of Information Science and Technology, Beijing University of Chemical Technology (Grant No. 0104/11170044115)

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  1. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, 100029, China

    Xian Shi

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Correspondence to Xian Shi.

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Shi, X. Entanglement polygon inequalities for pure states in qudit systems. Eur. Phys. J. Plus 138, 768 (2023). https://doi.org/10.1140/epjp/s13360-023-04399-y

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