Verifying Measures of Quantum Entropy

Abstract

This paper introduces a new measure of quantum entropy, called the effective quantum entropy (EQE). The EQE is an extension, to the quantum setting, of a recently derived classical generalized entropy. We present a thorough verification of its properties. As its predecessor, the EQE is a semi-strict quasi-concave function; it would be capable of generating many of the various measures of quantum entropy that are useful in practice. Thereafter, we construct a consistent estimator for our proposed measure and empirically test its estimation error, under different system dimensions and number of measurements. Overall, we build the grounds of the EQE, which will facilitate the analyses and verification of the next innovative quantum technologies.