Concavity, Core-concavity, Quasiconcavity: A Generalizing Framework for Entropy Measures

Américo, Arthur; Malacaria, Pasquale

doi:10.1109/csf51468.2021.00021

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2022

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“…On the other hand, Constantino Tsallis introduced the entropy in a nonextensive direction [13] as a generalization of the traditional Boltzmann-Gibbs entropy. Américo et al recently proposed a new generalizing framework for conditional entropies given concavity, core-concavity, or quasi-concavity [14]. In general, a helpful tool to construct a new type of entropy is convexity/or concavity.…”

Section: Introductionmentioning

confidence: 99%

Verifying Measures of Quantum Entropy

Pastor

Woo

2022

AppliedMath

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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.

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Section: Introductionmentioning

confidence: 99%