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Z-eigenvalue inclusion theorem of tensors and the geometric measure of entanglement of multipartite pure states

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Abstract

In our paper, we concentrate on the Z-eigenvalue inclusion theorem and its application in the geometric measure of entanglement of multipartite pure states. We present a new Z-eigenvalue inclusion theorem by virtue of the division and classification of tensor elements, and tighter bounds of Z-spectral radius of weakly symmetric nonnegative tensors are obtained. As applications, we present some theoretical upper and lower bounds of entanglement for symmetric pure state with nonnegative amplitudes for two kinds of geometric measures with different definitions, respectively.

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Acknowledgements

The authors are grateful to the anonymous referees for their helpful suggestions and comments. This work was supported by the National Natural Science Foundation of China (Grant nos. 11971413 and 11571292).

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Correspondence to Jianzhou Liu.

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Communicated by Jinyun Yuan.

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Xiong, L., Liu, J. Z-eigenvalue inclusion theorem of tensors and the geometric measure of entanglement of multipartite pure states. Comp. Appl. Math. 39, 135 (2020). https://doi.org/10.1007/s40314-020-01166-y

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  • DOI: https://doi.org/10.1007/s40314-020-01166-y

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