Connecting the generalized robustness and the geometric measure of entanglement

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.