Geometric measure of quantum entanglement for multipartite mixed states

S. Hu, Liqun Qi, Y. Song, Guofeng Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review


The geometric measure of quantum entanglement of a pure state, defined by its distance to the set of pure separable states, is extended to multipartite mixed states. We characterize the nearest disentangled mixed state to a given mixed state with respect to the geometric measure by means of a system of equations. The entanglement eigenvalue for a mixed state is introduced. And we show that, for a given mixed state, its nearest disentangled mixed state is associated with its entanglement eigenvalue. Two numerical examples are used to demonstrate the effectiveness of the proposed method.
Original languageEnglish
Pages (from-to)317-326
Number of pages10
JournalInternational journal of software and informatics
Issue number2018-04-03
Publication statusPublished - 2014


  • Quantum entanglement
  • Geometric measure
  • Optimization


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