Entanglement monotones for W-type states

In this article, we extend recent results concerning random-pair Einstein-Podolsky-Rosen distillation and the operational gap between separable operations (SEPs) and local operations with classical communication (LOCC). In particular, we consider the problem of obtaining bipartite maximal entanglement from an N-qubit W-class state (i.e., that of the form √x ₀|000+√x ₁|100++√x _n|00) when the target pairs are a priori unspecified. We show that when x ₀=0, the optimal probabilities for SEPs can be computed using semidefinite programming. On the other hand, to bound the optimal probabilities achievable by LOCC, we introduce entanglement monotones defined on the N-qubit W class of states. The LOCC monotones we construct can be increased by SEPs, and in terms of transformation success probability, we are able to quantify a gap as large as 37% between the two classes. Additionally, we demonstrate transformations ρ ^-n→σ ^-n that are feasible by SEP for any n but impossible by LOCC.