Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/18330
Title: Geometric measure of entanglement and U-eigenvalues of tensors
Authors: Ni, G
Qi, L 
Bai, M
Keywords: Geometric measure of entanglement
Symmetric real tensor
The best rank-one approximation
Unitary eigenvalue (U-eigenvalue)
Z-eigenvalue
Issue Date: 2014
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on matrix analysis and applications, 2014, v. 35, no. 1, p. 73-87 How to cite?
Journal: SIAM journal on matrix analysis and applications 
Abstract: We study tensor analysis problems motivated by the geometric measure of quantum entanglement. We define the concept of the unitary eigenvalue (U-eigenvalue) of a complex tensor, the unitary symmetric eigenvalue (US-eigenvalue) of a symmetric complex tensor, and the best complex rank-one approximation. We obtain an upper bound on the number of distinct US-eigenvalues of symmetric tensors and count all US-eigenpairs with nonzero eigenvalues of symmetric tensors. We convert the geometric measure of the entanglement problem to an algebraic equation system problem. A numerical example shows that a symmetric real tensor may have a best complex rankone approximation that is better than its best real rank-one approximation, which implies that the absolute-value largest Z-eigenvalue is not always the geometric measure of entanglement.
URI: http://hdl.handle.net/10397/18330
ISSN: 0895-4798
EISSN: 1095-7162
DOI: 10.1137/120892891
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