Skip to Main content Skip to Navigation
Journal articles

Some extensions of the uncertainty principle

Abstract : We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [I. Bialynicki-Birula, Formulation of the uncertainty relations in terms of the Rényi entropies, Physical Review A 74 (5) (2006) 052101] and Zozor et al. [S. Zozor, C. Vignat, On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles, Physica A 375 (2) (2007) 499-517]. Those inequalities can be considered as generalizations of the Heisenberg uncertainty principle, since they measure the mutual uncertainty of a wave function and its Fourier transform through their associated Rényi entropies with conjugated indices. We consider here the general case where the entropic indices are not conjugated, in both cases where the state space is discrete and continuous: we discuss the existence of an uncertainty inequality depending on the location of the entropic indices alpha and beta in the plane (alpha,beta). Our results explain and extend a recent study by Luis [A. Luis, Quantum properties of exponential states, Physical Review A 75 (2007) 052115], where states with quantum fluctuations below the Gaussian case are discussed at the single point (2, 2).
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00282882
Contributor : Steeve Zozor <>
Submitted on : Wednesday, May 28, 2008 - 4:24:36 PM
Last modification on : Wednesday, May 13, 2020 - 4:30:04 PM

Links full text

Identifiers

Citation

Steeve Zozor, Mariela Portesi, Christophe Vignat. Some extensions of the uncertainty principle. Physica A: Statistical Mechanics and its Applications, Elsevier, 2008, 37 (19-20), pp.4800-4808. ⟨10.1016/j.physa.2008.04.010⟩. ⟨hal-00282882⟩

Share

Metrics

Record views

843