New Z -Eigenvalue Localization Set for Tensor and Its Application in Entanglement of Multipartite Quantum States

Liang Xiong, Zhanfeng Jiang, Jianzhou Liu and Qi Qin
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Liang Xiong: Key Laboratory of Optoelectronic Devices and Systems, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
Zhanfeng Jiang: Key Laboratory of Optoelectronic Devices and Systems, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
Jianzhou Liu: Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
Qi Qin: Key Laboratory of Optoelectronic Devices and Systems, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China

Mathematics, 2022, vol. 10, issue 15, 1-12

Abstract: This study focuses on tensor Z -eigenvalue localization and its application in the geometric measure of entanglement for multipartite quantum states. A new Z -eigenvalue localization theorem and the bounds for the Z-spectral radius are derived, which are more precise than some of the existing results. On the other hand, we present theoretical bounds of the geometric measure of entanglement for a weakly symmetric multipartite quantum state with non-negative amplitudes by virtue of different distance measures. Numerical examples show that these conclusions are superior to the existing results in quantum physics in some cases.

Keywords: Z-eigenvalue; non-negative tensors; spectral radius; geometric measure of entanglement (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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