Eur. Phys. J. B 52, 191-198 (2006)
https://doi.org/10.1140/epjb/e2006-00280-0

New uncertainty relations for tomographic entropy: application to squeezed states and solitons

¹ Istituto di Cibernetica “Eduardo Caianiello” del CNR Comprensorio “A. Olivetti” Fabbr. 70, Via Campi Flegrei, 34, I-80078 Pozzuoli (NA), Italy
² Dipartimento di Scienze Fisiche, Università Federico II and INFN Sezione di Napoli, Complesso Universitario di M.S. Angelo, via Cintia, 80126 Napoli, Italy
³ P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow, 119991, Russia

Corresponding authors: ^a s.denicola@cib.na.cnr.it - ^b renato.fedele@na.infn.it - ^c mmanko@sci.lebedev.ru - ^d manko@na.infn.it manko@sci.lebedev.ru

Received: 11 May 2006
Published online: 7 July 2006

Abstract

Using the tomographic probability distribution (symplectic tomogram) describing the quantum state (instead of the wave function or density matrix) and properties of recently introduced tomographic entropy associated with the probability distribution, the new uncertainty relation for the tomographic entropy is obtained. Examples of the entropic uncertainty relation for squeezed states and solitons of the Bose-Einstein condensate are considered.