Maximal singlet fraction vs. maximal achievable fidelity as proper entanglement measures

TL;DR

This paper compares different entanglement measures for 2-qubit states, showing that maximal achievable fidelity aligns better with concurrence than maximal singlet fraction, highlighting its suitability as an entanglement measure.

Contribution

It demonstrates that maximal achievable fidelity is a more consistent entanglement measure than maximal singlet fraction for certain 2-qubit states.

Findings

MAF aligns better with concurrence than MSF

MSF and concurrence can behave oppositely

MAF satisfies key features of a good entanglement measure

Abstract

We review some parametric families of 2-qubit states for which concurrence and maximal singlet fraction (MSF) have different and even opposite behaviour. For states considered in this work, maximal achievable fidelity (MAF), a quantity derived by Verstraete and Verschelde in 2003, shows a better agreement with concurrence and complies with important features required to be considered a good entanglement measure.