Weak quantum correlation quantifiers with generalized entropies

Abstract

We define a broad class of quantum correlation quantifiers (QCQs) based on generalized entropies and projective measurements and compare it with the case where the measurements are weak for a broad class of weak measurements (WMs) that operate in finite-dimensional systems. We also propose a general way to define a WM using a measure of disturbance and show that the QCQs by these measurements are majorized by those defined by the projective ones. Our result strengthens the hypothesis that WMs reveal fewer quantum correlations than projective measurements in a way that depends very little on the type of the QCQ. Finally, we prove that the quantifier is increasing with the force of the measurement and, as an example, we analytically calculate a particular case using the linear entropy.