A Class of Distance-Based Incompatibility Measures for Quantum Measurements

Abstract

We discuss a recently proposed class of incompatibility measures for quantum measurements, which is based on quantifying the effect of measurements of one observable on the statistics of the outcome of another. We summarize the properties of this class of measures, and present a tight upper bound for the incompatibility of any set of projective measurements in finite dimensions. We also discuss non-projective measurements, and give a non-trivial upper bound on the mutual incompatibility of a pair of Lüders instruments. Using the example of incompatible observables that commute on a subspace, we elucidate how this class of measures goes beyond uncertainty relations in quantifying the mutual incompatibility of quantum measurements.