This article introduces a new metric called vertex entanglement (VE), which quantifies the impact of individual vertices on the spectral entropy of a network. VE is derived from quantum information theory and is used to identify key players in complex networks. The metric is closely related to network robustness and information transmission ability. It is applied to network dismantling and autism spectrum disorder (ASD) diagnosis. VE is defined as the difference in spectral entropy between a network and a perturbed version of it. The study shows that VE is effective in identifying key vertices and outperforms existing algorithms in network dismantling. Additionally, VE is used to detect differences in brain networks between ASD and typical control participants, with significant differences in hub disruption indices. The results suggest that VE could be a useful tool for ASD diagnosis. The study also explores the application of VE in complex systems, including the integration of quantum information theory with network science. The results demonstrate that VE is a promising metric for assessing the importance of vertices in complex systems. The study also discusses the computational efficiency of VE and its potential for practical applications. The findings indicate that VE is a valuable tool for analyzing complex networks and has potential applications in various fields, including network science and neuroscience.This article introduces a new metric called vertex entanglement (VE), which quantifies the impact of individual vertices on the spectral entropy of a network. VE is derived from quantum information theory and is used to identify key players in complex networks. The metric is closely related to network robustness and information transmission ability. It is applied to network dismantling and autism spectrum disorder (ASD) diagnosis. VE is defined as the difference in spectral entropy between a network and a perturbed version of it. The study shows that VE is effective in identifying key vertices and outperforms existing algorithms in network dismantling. Additionally, VE is used to detect differences in brain networks between ASD and typical control participants, with significant differences in hub disruption indices. The results suggest that VE could be a useful tool for ASD diagnosis. The study also explores the application of VE in complex systems, including the integration of quantum information theory with network science. The results demonstrate that VE is a promising metric for assessing the importance of vertices in complex systems. The study also discusses the computational efficiency of VE and its potential for practical applications. The findings indicate that VE is a valuable tool for analyzing complex networks and has potential applications in various fields, including network science and neuroscience.