title: One-parameter class of uncertainty relations based on entropy power.
abstract: 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.
authors.affiliation: FNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech Republic.|ITP, Freie Universität Berlin, Arnimallee 14 D-14195 Berlin, Germany.
authors.forename: Petr
authors.initials: P
authors.lastname: Jizba
authors.affiliation: Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China.
authors.forename: Yue
authors.initials: Y
authors.lastname: Ma
authors.affiliation: Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom.
authors.forename: Anthony
authors.initials: A
authors.lastname: Hayes
authors.affiliation: Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom.
authors.forename: Jacob A
authors.initials: JA
authors.lastname: Dunningham