Separability of multi-qubit states in terms of diagonal and anti-diagonal entries

Abstract

We give separability criteria for general multi-qubit states in terms of diagonal and anti-diagonal entries. We define two numbers which are obtained from diagonal and anti-diagonal entries, respectively, and compare them to get criteria. They give rise to characterizations of separability when all the entries are zero except for diagonal and anti-diagonal, like Greenberger–Horne–Zeilinger diagonal states. The criteria are strong enough to detect nonzero volume of entanglement with positive partial transposes.