Entanglement witness

Recently I read a article quant-ph/0503037 written by Marcin Wiesniak, Vlato Vedral and Caslav Brukner. Here is the abstract:

We show that, when measured along orthogonal spatial directions, magnetic susceptibility can reveal entanglement between individual constituents of a solid, while magnetisation describes their local properties. We then show that these two thermodynamical quantities satisfy complementary relation in the quantum-mechanical sense. It describes sharing of (quantum) information in the solid between entanglement and local properties of its individual constituents. Magnetic susceptibility is shown to be universal macroscopic entanglement witness that can be applied independently of the model of the solid (without the knowledge of its Hamiltonian).

The most important result of this article, in my opinion, is the quantum complementary relation. That is the sum of the entanglement and the local properties S=frac{langle rightarrow{M}rangle^2}{N^2}. This article also given a criterion to estimate the solid state system contains entanglement or not. If the magnetic susceptibility bigger than a critical value, there must be entanglement in the system. As we know, susceptibility has been experimental routime for long time. So using the result of the article, we can detect the entanglement in the solid system. I think this is an important result. In fact, this article told us that magntetization only described the local feather of a solid, but susceptibility related with the global entanglement of the solid system.

I guess that the localizalbe entanglment(LE) defined in the recent article PRA 71, 042306 (2005) may have some relation with the result of the article above. The lower bound of LE connects with a correlation function. As we kown, susceptibility is some kind of correlation in the solid system. If I dig deeply in this, I think I can reveal this relation.