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Computing Geometric Measure of Entanglement for Symmetric Pure States via the Jacobian SDP Relaxation Technique

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Abstract

The problem of computing geometric measure of quantum entanglement for symmetric pure states can be regarded as the problem of finding the largest unitary symmetric eigenvalue (US-eigenvalue) for symmetric complex tensors, which can be taken as a multilinear optimization problem in complex number field. In this paper, we convert the problem of computing the geometric measure of entanglement for symmetric pure states to a real polynomial optimization problem. Then we use Jacobian semidefinite relaxation method to solve it. Some numerical examples are presented.

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Acknowledgments

The authors thank the two anonymous referees for their very useful comments.

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Authors and Affiliations

  1. College of Science, National University of Defense Technology, Changsha, 410073, China

    Bing Hua, Gu-Yan Ni & Meng-Shi Zhang

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  1. Bing Hua
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  2. Gu-Yan Ni
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  3. Meng-Shi Zhang
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Correspondence to Gu-Yan Ni.

Additional information

This work was supported by the Research Programme of National University of Defense Technology (No. ZK16-03-45).

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Hua, B., Ni, GY. & Zhang, MS. Computing Geometric Measure of Entanglement for Symmetric Pure States via the Jacobian SDP Relaxation Technique. J. Oper. Res. Soc. China 5, 111–121 (2017). https://doi.org/10.1007/s40305-016-0135-1

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