New <i>Z</i>-Eigenvalue Localization Set for Tensor and Its Application in Entanglement of Multipartite Quantum States
Liang Xiong,
Zhanfeng Jiang,
Jianzhou Liu,
Qi Qin
Affiliations
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
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.
