New class of entropy-power-based uncertainty relations

8th International Workshop DICE2016: Spacetime - Matter - Quantum Mechanics

物理学;力学

Jizba, P.^1 ; Hayes, A.^2 ; Dunningham, J.A.^2

FNSPE, Czech Technical University in Prague, Behová 7, Praha 1

115 19, Czech Republic^1

Department of Physics and Astronomy, University of Sussex, Brighton

BN1 9QH, United Kingdom^2

关键词: Heavy-tailed;    Information distributions;    Shannon entropy;    Squeezed state;    Uncertainty relation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/880/1/012054/pdf
DOI  :  10.1088/1742-6596/880/1/012054

学科分类：力学，机械学

来源: IOP

【 摘 要 】

We use the concept of entropy power to introduce a new one-parameter class of information-theoretic uncertainty relations. This class constitutes an infinite hierarchy of uncertainty relations, which allows to determine the shape of the underlying information-distribution function by measuring the relevant entropy powers. The efficiency of such uncertainty relations in quantum mechanics is illustrated with two examples: superpositions of two squeezed states and the Lévy-type heavy-tailed wave function. Improvement over both the variance-based and Shannon entropy based uncertainty relations is demonstrated in both these cases.