Exact calculation of robustness of entanglement via convex semi-definite programming

Abstract

In general the calculation of robustness of entanglement for the mixed entangled quantum states is rather difficult to handle analytically. Using the the convex semi-definite programming method, the robustness of entanglement of some mixed entangled quantum states such as: $2\otimes 2$ Bell decomposable (BD) states, a generic two qubit state in Wootters basis, iso-concurrence decomposable states, $2\otimes 3$ Bell decomposable states, $d\otimes d$ Werner and isotropic states, a one parameter $3\otimes 3$ state and finally multi partite isotropic state, is calculated exactly, where thus obtained results are in agreement with those of :$2\otimes 2$ density matrices, already calculated by one of the authors in \cite{Bell1,Rob3}. Also an analytic expression is given for separable states that wipe out all entanglement and it is further shown that they are on the boundary of separable states as pointed out in \cite{du}. {\bf Keywords: Robustness of entanglement, Semi-definite programming, Bell decomposable states, Werner and isotropic states.}