Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3643
Articles: 2'487'895
Articles rated: 2609

29 March 2024
 
  » arxiv » 1012.3786

 Article overview


A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces
Remigiusz Augusiak ; Jordi Tura ; Maciej Lewenstein ;
Date 17 Dec 2010
AbstractEntanglement witnesses (EWs) constitute one of the most important entanglement detectors in quantum systems. Nevertheless, their complete characterization, in particular with respect to the notion of optimality, is still missing, even in the decomposable case. Here we show that for any qubit-qunit decomposable EW (DEW) W the three statements are equivalent: (i) the set of product vectors obeying <e,f|W|e,f>=0 span the corresponding Hilbert space, (ii) W is optimal, (iii) W=Q^{Gamma} with positive Q supported on a completely entangled subspace (CES). While, implications $(i)Rightarrow(ii)$ and $(ii)Rightarrow(iii)$ are known, here we prove that (iii) implies (i). This is a consequence of a more general fact saying that product vectors orthogonal to any CES in C^2otimes C^n span, after partial conjugation, the whole space. On the other hand, already in the case of C^3otimes C^3 Hilbert space, there exist DEWs for which (iii) does not imply (i). Consequently, either (i) does not imply (ii), or (ii) does not imply (iii), and the above transparent characterization obeyed by qubit-qunit DEWs, does not hold in general.
Source arXiv, 1012.3786
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser claudebot






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica