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One-parameter class of uncertainty relations based on entropy power
Petr Jizba1,2, Yue Ma3, Anthony Hayes4
1FNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech Republic.
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.
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