Geometric measure of entanglement and its applications to multi-partite states and quantum phase transitions

          @misc{ pirsa_PIRSA:07010012,
            doi = {10.48660/07010012},
            url = {https://pirsa.org/07010012},
            author = {Wei, Tzu-Chieh},
            keywords = {Quantum Information},
            language = {en},
            title = {Geometric measure of entanglement and its applications to multi-partite states and quantum phase transitions},
            publisher = {Perimeter Institute},
            year = {2007},
            month = {jan},
            note = {PIRSA:07010012 see, \url{https://pirsa.org}}
          }
          

Abstract

A multi-partite entanglement measure is constructed via the distance or angle of the pure state to its nearest unentangled state. The extention to mixed states is made via the convex-hull construction, as is done in the case of entanglement of formation. This geometric measure is shown to be a monotone. It can be calculated for various states, including arbitrary two-qubit states, generalized Werner and isotropic states in bi-partite systems. It is also calculated for various multi-partite pure and mixed states, including ground states of some physical models and states generated from quantum alogrithms, such as Grover's. A specific application to a spin model with quantum phase transistions will be presented in detail.The connection of the geometric measure to other entanglement properties will also be discussed.