Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement

Mengshi Zhang, Guyan Ni, Guofeng Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

The purpose of this paper is to study the problem of computing unitary eigenvalues (U-eigenvalues) of non-symmetric complex tensors. By means of symmetric embedding of complex tensors, the relationship between U-eigenpairs of a non-symmetric complex tensor and unitary symmetric eigenpairs (US-eigenpairs) of its symmetric embedding tensor is established. An Algorithm 3.1 is given to compute the U-eigenvalues of non-symmetric complex tensors by means of symmetric embedding. Another Algorithm 3.2, is proposed to directly compute the U-eigenvalues of non-symmetric complex tensors, without the aid of symmetric embedding. Finally, a tensor version of the well-known Gauss–Seidel method is developed. Efficiency of these three algorithms are compared by means of various numerical examples. These algorithms are applied to compute the geometric measure of entanglement of quantum multipartite non-symmetric pure states.

Original languageEnglish
Pages (from-to)779-798
Number of pages20
JournalComputational Optimization and Applications
Volume75
Issue number3
DOIs
Publication statusPublished - Apr 2020

Keywords

  • Complex tensor
  • Geometric measure of entanglement
  • Iterative method
  • Unitary eigenvalue

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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