New class of entropy-power-based uncertainty relations

[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.

[发布机构] 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

[效力级别] 力学 [学科分类] 力学，机械学

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