One-parameter class of uncertainty relations based on entropy power

Abstract

We use the concept of entropy power to derive a new one-parameter class of information-theoretic uncertainty relations for pairs of conjugate observables in an infinite-dimensional Hilbert space. This class constitutes an infinite tower of higher-order statistics uncertainty relations, which allows one in principle to determine the shape of the underlying information-distribution function by measuring the relevant entropy powers. We illustrate the capability of the new class by discussing two examples: superpositions of vacuum and squeezed states and the Cauchy-type heavy-tailed wave function.

arXiv comment13 pages (including supplementary material), 4 figures

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