EXACT CALCULATION OF ROBUSTNESS OF ENTANGLEMENT VIA CONVEX SEMI-DEFINITE PROGRAMMING

In general, the calculation of robustness of entanglement for the mixed entangled quantum states is rather difficult to handle analytically. Using the convex semi-definite programming method, we claculate exactly the robustness of entanglement of some mixed entangled quantum states such as the generic two-qubit state in the Wootters basis, 2 ⊗ 2 Bell decomposable (BD) states, iso-concurrence decomposable states, 2 ⊗ 3 Bell decomposable states, d ⊗ d Werner and isotropic states, a one parameter 3 ⊗ 3 state and a multi-partite isotropic state. The results are in agreement with those of 2 ⊗ 2 density matrices and have already been calculated in Refs. 1 and 2. Also, an analytic expression is given for separable states that wipe out all the entanglements. It is further shown that they are on the boundary of separable states, as pointed out in Ref. 3.