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

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