Connecting the generalized robustness and the geometric measure of entanglement

Abstract

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 $R_g(\rho )$ based only on the purity of $\rho$ and its maximal overlap to a separable state. As we will see it is also possible to express this lower bound in terms of $E_{GME}$.

arXiv comment4 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

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