

Preprint 79/2013
Criterion of Local Unitary Equivalence for Multipartite States
Ting-Gui Zhang, Ming-Jing Zhao, Ming Li, Shao-Ming Fei, and Xianqing Li-Jost
Contact the author: Please use for correspondence this email.
Submission date: 14. Aug. 2013
Pages: 14
published in: Physical review / A, 88 (2013) 4, art-no. 042304
DOI number (of the published article): 10.1103/PhysRevA.88.042304
Bibtex
PACS-Numbers: 03.67.-a, 02.20.Hj, 03.65.-w
Download full preprint: PDF (167 kB)
Abstract:
We study the local unitary equivalence of arbitrary dimensional multipartite quantum mixed states.
We present a necessary and sufficient criterion of the local unitary equivalence for general
multipartite states based on matrix realignment.
The criterion is shown to be operational even for particularly degenerated states
by detailed examples. Besides, explicit expressions of the local unitary operators are constructed
for locally equivalent states.
In complement to the criterion, an alternative approach
based on partial transposition of matrices
are also given, which makes the criterion more effective in dealing with generally degenerated mixed states.