One-parameter class of uncertainty relations based on entropy power - Jizba, Petr; Ma, Yue; Hayes, Anthony; Dunningham, Jacob A (Physical review. E, 2016)
We use the concept of entropy power to derive a 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 this class by discussing two examples: superpositions of vacuum and squeezed states and the Cauchy-type heavy-tailed wave function.