An alternative steepest direction method for the optimization in evaluating geometric discord

Y.J. Wang, Liqun Qi, S.L. Luo, Y. Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review


We address the evaluation of geometric discord of bipartite quantum states arising from quantum information theory. The problem corresponds to finding the best approximation of the orthogonal decomposition of a partially Hermite fourth-order tensor. By discussing the optimality condition of the problem, we reduce it to a homogenous polynomial optimization problem on the product of two unitary matrices. Based on the Riemannian manifold and Lie group theory, we propose an alternative steepest direction method for the problem. Numerical experiments show the efficiency of the method.
Original languageEnglish
Pages (from-to)137-149
Number of pages13
JournalPacific Journal of Optimization
Issue number1
Publication statusPublished - 2014


  • Geometric discord
  • Unitary matrix constraints
  • Geodesic
  • Steepest direction method

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Control and Optimization

Cite this