PIRSA:07010012 Scientific Series Quantum Information

DOI10.48660/07010012

Series: Perimeter Institute Quantum Discussions

Wei, T. (2007). Geometric measure of entanglement and its applications to multi-partite states and quantum phase transitions. Perimeter Institute. https://pirsa.org/07010012

Wei, Tzu-Chieh. Geometric measure of entanglement and its applications to multi-partite states and quantum phase transitions. Perimeter Institute, Jan. 17, 2007, https://pirsa.org/07010012 

@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.

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