set of general quantum operations $\{B_{ij}^{(1)}\}$, satisfying $\sum_j (B_{ij}^{(1)})^{\dagger} B_{ij}^{(1)} = I_B$ on his part belonging to the Hilbert space $\mathcal{H}_B$. This joint operation along with the classical communication is called one-way LOCC. Furthermore, Bob can send his result $j$ to Alice, and she can choose another set of local operations $\{A_{ijk}^{(2)}\}$, satisfying $\sum_k (A_{ijk}^{(2)})^{\dagger} A_{ijk}^{(2)} = I_A$, according to Bob’s outcome. They can continue this process as long as required, and the entire operation is termed as LOCC, or two-way LOCC. The operators $I_A$ and $I_B$ are the identity operators on $\mathcal{H}_A$ and $\mathcal{H}_B$ respectively.

Entangled states cannot be prepared by two parties if only LOCC is allowed between them. To prepare such states, the physical systems must be brought together to interact [^1].

The question whether a given bipartite state is separable or not turns out to be quite complicated. Among the difficulties, we notice that for an arbitrary state $\rho_{AB}$, there is no stringent bound on the value of $K$ in Eq. (\[eqn:sepmixed\]), which is only limited by the Caratheodory theorem to be $K \leq (\dim {\cal H} )^2$ with ${\cal H} = {\cal H}_A \otimes {\cal H}_B$ (see [@Pawelbound; @karnas00]). Although the general answer to the 