Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/43976
Title: Computing the geometric measure of entanglement of multipartite pure states by means of non-negative tensors
Authors: Hu, S
Qi, L 
Zhang, G 
Issue Date: 2016
Publisher: American Physical Society
Source: Physical review. A, Atomic, molecular, and optical physics, 2016, v. 93, no. 1, 012304 How to cite?
Journal: Physical review. A, Atomic, molecular, and optical physics 
Abstract: The geometric measure of entanglement for pure states has attracted much attention. On the other hand, the spectral theory of non-negative tensors (hypermatrices) has been developed rapidly. In this paper, we show how the spectral theory of non-negative tensors can be applied to the study of the geometric measure of entanglement for pure states. For symmetric pure multipartite qubit or qutrit states an elimination method is given. For symmetric pure multipartite qudit states, a numerical algorithm with randomization is presented. We also show that a nonsymmetric pure state can be augmented to a symmetric one whose amplitudes can be encoded in a non-negative symmetric tensor, so the geometric measure of entanglement can be calculated. Several examples, such as mGHZ states, W states, inverted W states, qudits, and nonsymmetric states, are used to demonstrate the power of the proposed methods. Given a pure state, one can always find a change of basis (a unitary transformation) so that all the probability amplitudes of the pure state are non-negative under the new basis. Therefore, the methods proposed here can be applied to a very wide class of multipartite pure states.
URI: http://hdl.handle.net/10397/43976
ISSN: 1050-2947
EISSN: 1094-1622
DOI: 10.1103/PhysRevA.93.012304
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

4
Last Week
0
Last month
Citations as of Sep 24, 2017

WEB OF SCIENCETM
Citations

5
Last Week
0
Last month
Citations as of Sep 21, 2017

Page view(s)

25
Last Week
2
Last month
Checked on Sep 24, 2017

Google ScholarTM

Check

Altmetric



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.