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

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.