Partial transpose as a direct link between concurrence and negativity

TL;DR

This paper explores the relationship between concurrence and negativity in bipartite quantum states, revealing their close connection through the partial transpose and providing unified estimates for mixed-state entanglement.

Contribution

It demonstrates the direct link between concurrence and negativity via the partial transpose, unifying different entanglement measures and offering new bounds for mixed states.

Findings

Concurrence and negativity are closely related through the partial transpose.

Unified estimates for mixed-state concurrence are derived.

Connections between different entanglement quantifiers are clarified.

Abstract

Detection of entanglement in bipartite states is a fundamental task in quantum information. The first method to verify entanglement in mixed states was the partial-transpose criterion. Subsequently, numerous quantifiers for bipartite entanglement were introduced, among them concurrence and negativity. Surprisingly, these quantities are often treated as distinct or independent of each other. The aim of this contribution is to highlight the close relations between these concepts, to show the connections between seemingly independent results, and to present various estimates for the mixed-state concurrence within the same framework.