New Z-Eigenvalue Localization Set for Tensor and Its Application in Entanglement of Multipartite Quantum States
- Resource Type
- article
- Authors
- Liang Xiong; Zhanfeng Jiang; Jianzhou Liu; Qi Qin
- Source
- Mathematics, Vol 10, Iss 2624, p 2624 (2022)
- Subject
- Z-eigenvalue
non-negative tensors
spectral radius
geometric measure of entanglement
Mathematics
QA1-939
- Language
- English
- ISSN
- 2227-7390
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.