Positive maps, majorization, entropic inequalities, and detection of entanglement

Details Positive maps, majorization, entropic inequalities, and detection of entanglement Positive maps, majorization, entropic inequalities, and detection of entanglement

2008-11-21

arxiv.org/abs/0811.3604v3

New Journal of Physics 11, 053018 (2009)

Physics

Quantum Physics

the published version, 25 pages in NJP format, 6 figures

Scientific paper

10.1088/1367-2630/11/5/053018

In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that any positive map $\Lambda:M_{d}(\mathbb{C})\to M_{d}(\mathbb{C})$ can be written as the difference between two completely positive maps $\Lambda=\Lambda_{1}-\Lambda_{2}$, we propose a possible way to generalize the Nielsen--Kempe majorization criterion. Then we present two methods of derivation of some general classes of entropic inequalities useful for the detection of entanglement. While the first one follows from the aforementioned generalized majorization relation and the concept of the Schur--concave decreasing functions, the second is based on some functional inequalities. What is important is that, contrary to the Nielsen--Kempe majorization criterion and entropic inequalities, our criteria allow for the detection of entangled states with positive partial transposition when using indecomposable positive maps. We also point out that if a state with at least one maximally mixed subsystem is detected by some necessary criterion based on the positive map $\Lambda$, then there exist entropic inequalities derived from $\Lambda$ (by both procedures) that also detect this state. In this sense, they are equivalent to the necessary criterion $[I\ot\Lambda](\varrho_{AB})\geq 0$. Moreover, our inequalities provide a way of constructing multi--copy entanglement witnesses and therefore are promising from the experimental point of view. Finally, we discuss some of the derived inequalities in the context of recently introduced protocol of state merging and possibility of approximating the mean value of a linear entanglement witness.

Affiliated with

Also associated with

No associations

Rating

Positive maps, majorization, entropic inequalities, and detection of entanglement does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive maps, majorization, entropic inequalities, and detection of entanglement, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive maps, majorization, entropic inequalities, and detection of entanglement will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-163817