Connecting the generalized robustness and the geometric measure of entanglement
Abstract
Description
The main goal of this paper is to provide a connection between the generalized robustness of entanglement ($R_g$) and the geometric measure of entanglement ($E_{GME}$). First, we show that the generalized robustness is always higher than or equal to the geometric measure. Then we find a tighter lower bound to $R_g(ρ)$ based only on the purity of $ρ$ and its maximal overlap to a separable state. As we will see it is also possible to express this lower bound in terms of $E_{GME}$.
4 pages, 2 figures. Comments welcome. v2: text improved - some completely symmetric states were used to illustrate the results. Comments are always welcome! v3: minor changes. Accepted by Phys. Rev. A. v4: results on symmetric states fixed
4 pages, 2 figures. Comments welcome. v2: text improved - some completely symmetric states were used to illustrate the results. Comments are always welcome! v3: minor changes. Accepted by Phys. Rev. A. v4: results on symmetric states fixed