A family of separability criteria and lower bounds of concurrence

TL;DR

This paper introduces a family of separability criteria based on Ky Fan norms, providing analytical lower bounds for concurrence and negativity, advancing entanglement detection methods in quantum information theory.

Contribution

It develops a new family of separability criteria using Ky Fan norms and derives analytical lower bounds for entanglement measures in bipartite quantum states.

Findings

Criteria are equivalent to the enhanced realignment criterion for real density matrices.

Provides analytical lower bounds for concurrence in arbitrary dimensions.

Offers bounds for convex-roof extended negativity.

Abstract

The problem on detecting the entanglement of a bipartite state is significant in quantum information theory. In this article, we apply the Ky Fan norm to the revised realignment matrix of a bipartite state. Specifially, we consider a family of separable criteria for bipartite states, and present when the density matrix corresponds to a state is real, the criteria is equivalent to the enhanced realignment criterion. Moreover, we present analytical lower bounds of concurrence and the convex-roof extended negativity for arbitrary dimensional systems.