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

TL;DR

This paper introduces new criteria for determining the separability of multi-qubit states based on their diagonal and anti-diagonal entries, providing a practical way to identify entanglement.

Contribution

It presents novel separability criteria using diagonal and anti-diagonal entries, applicable to general multi-qubit states, including specific classes like GHZ diagonal states.

Findings

Criteria successfully characterize separability in certain states.

Method detects nonzero volume of entanglement with positive partial transposes.

Provides a practical approach for analyzing multi-qubit entanglement.

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 is strong enough to get nonzero volume of entanglement with positive partial transposes.