Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/93305
Title: | Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement | Authors: | Zhang, M Ni, G Zhang, G |
Issue Date: | Apr-2020 | Source: | Computational optimization and applications, Apr. 2020, v. 75, no. 3, p. 779-798 | 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. | Keywords: | Complex tensor Geometric measure of entanglement Iterative method Unitary eigenvalue |
Publisher: | Springer | Journal: | Computational optimization and applications | ISSN: | 0926-6003 | EISSN: | 1573-2894 | DOI: | 10.1007/s10589-019-00126-5 | Rights: | © Springer Science+Business Media, LLC, part of Springer Nature 2019 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10589-019-00126-5 |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Zhang_Iterative_Methods_Computing.pdf | Pre-Published version | 872.18 kB | Adobe PDF | View/Open |
Page views
54
Last Week
0
0
Last month
Citations as of May 5, 2024
Downloads
39
Citations as of May 5, 2024
SCOPUSTM
Citations
5
Citations as of Apr 26, 2024
WEB OF SCIENCETM
Citations
5
Citations as of May 2, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.