Separability in terms of a single entanglement witness
Piotr Badziąg, Paweł Horodecki, Ryszard Horodecki, Remigiusz Augusiak · Physical Review A · 2013
The separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state $\ensuremath{\varrho}$ is separable if and only if a specially constructed entanglement witness ${W}_{\ensuremath{\varrho}}$ is weakly optimal, i.e., its expectation value vanishes on at least one product vector. Interestingly, the witness can always be chosen to be decomposable. Our result changes the conceptual aspect of the separability problem and raises some questions about the properties of positive maps.