Negativity and Concurrence of mixed 2X2 states

TL;DR

This paper investigates the relationship between concurrence and negativity as measures of entanglement in 2x2 mixed states, proving a conjecture and characterizing states with specific entanglement measure relations.

Contribution

It proves that concurrence is never smaller than negativity and characterizes states where these measures are equal or differ maximally.

Findings

Concurrence ≥ negativity for all 2x2 mixed states

States with equal concurrence and negativity are fully characterized

Maximum difference between concurrence and negativity is identified for certain states

Abstract

We consider two measures of entanglement of mixed bipartite states of dimension 2X2: concurrence and negativity. We first prove the conjecture of Eisert and Plenio that concurrence can never be smaller than negativity. We then characterise all states for which concurrence equals negativity and also those states for which the difference between concurrence and negativity is maximal (keeping either the concurrence fixed, or the participation ratio R=1/trace(rho^2)).