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An alternative steepest direction method for the optimization in evaluating geometric discord. (English) Zbl 1285.81008
Summary: 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.

81P40 Quantum coherence, entanglement, quantum correlations
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
65F99 Numerical linear algebra
65K10 Numerical optimization and variational techniques
15A69 Multilinear algebra, tensor calculus
14M15 Grassmannians, Schubert varieties, flag manifolds
90C53 Methods of quasi-Newton type
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