Quantum metrology and quantum correlations

Abstract

Given a physical system to define a suitable measurement process on it constitutes one of the most crucial and challenging issues in physics. According to the particular theory under consideration, taking measurements has more or fewer subtleties but one ubiquitous concept for every physical theory is the uncertainty. In quantum mechanics, it is possible to identify a fundamental unpredictability given by Heisenberg uncertainty relations and the indistinguishability of quantum states, together with a practical uncertainty related to unavoidable errors in the measurement process. Considering only these fundamental ties, the estimation of unknown values of physical magnitudes has well-defined precision limits. The Cramer–Rao bound is a cornerstone for the analysis of these restrictions and an irreplaceable tool to determine the most accurate measurement procedures. On the quantum side, there exist quantum correlations known as entanglement and quantum discord which bring new ways to overcome the classical precision limits. Quantum metrology is a relatively young emerging area whose main aim is to study how to improve parameter estimation theory by using quantum correlations present in multipartite systems.