On a conjecture regarding Fisher information

Fisher's information measure I plays a very important role in diverse areas of theoretical physics. The associated measures I<SUB>x</SUB> and I<SUB>p</SUB>, as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Plastino, Ángel Luis, Bellomo, Guido, Plastino, Ángel Ricardo
Formato: Articulo
Lenguaje:Inglés
Publicado: 2015
Materias:
Ciencias Exactas
Entropy
Fisher information
Complexity
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/85739
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-85739
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Entropy
Fisher information
Complexity
spellingShingle Ciencias Exactas
Entropy
Fisher information
Complexity
Plastino, Ángel Luis
Bellomo, Guido
Plastino, Ángel Ricardo
On a conjecture regarding Fisher information
topic_facet Ciencias Exactas
Entropy
Fisher information
Complexity
description Fisher's information measure I plays a very important role in diverse areas of theoretical physics. The associated measures I<SUB>x</SUB> and I<SUB>p</SUB>, as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product I<SUB>x</SUB>I<SUB>p</SUB> has been conjectured to exhibit a nontrivial lower bound in Hall (2000). More explicitly, this conjecture says that for any pure state of a particle in one dimension I<SUB>x</SUB>I<SUB>p</SUB> ≥ 4. We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schrödinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schrödinger equation. We also conjecture that any normalizable time-dependent solution of this equation verifies I<SUB>x</SUB>I<SUB>p</SUB> → 0 for t → ∞.
format Articulo
Articulo
author Plastino, Ángel Luis
Bellomo, Guido
Plastino, Ángel Ricardo
author_facet Plastino, Ángel Luis
Bellomo, Guido
Plastino, Ángel Ricardo
author_sort Plastino, Ángel Luis
title On a conjecture regarding Fisher information
title_short On a conjecture regarding Fisher information
title_full On a conjecture regarding Fisher information
title_fullStr On a conjecture regarding Fisher information
title_full_unstemmed On a conjecture regarding Fisher information
title_sort on a conjecture regarding fisher information
publishDate 2015
url http://sedici.unlp.edu.ar/handle/10915/85739
work_keys_str_mv AT plastinoangelluis onaconjectureregardingfisherinformation
AT bellomoguido onaconjectureregardingfisherinformation
AT plastinoangelricardo onaconjectureregardingfisherinformation
bdutipo_str Repositorios
_version_ 1764820488827174914

Ejemplares similares