On a conjecture regarding Fisher information
- Autores
- Plastino, Ángel Luis; Bellomo, Guido; Plastino, Ángel Ricardo
- Año de publicación
- 2015
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Fisher's information measure I plays a very important role in diverse areas of theoretical physics. The associated measures Ix and Ip, as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product IxIp 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 IxIp ≥ 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 IxIp → 0 for t → ∞.
Facultad de Ciencias Exactas
Instituto de Física La Plata - Materia
-
Ciencias Exactas
Entropy
Fisher information
Complexity - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/85739
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On a conjecture regarding Fisher informationPlastino, Ángel LuisBellomo, GuidoPlastino, Ángel RicardoCiencias ExactasEntropyFisher informationComplexityFisher'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 → ∞.Facultad de Ciencias ExactasInstituto de Física La Plata2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/85739enginfo:eu-repo/semantics/altIdentifier/issn/1687-9120info:eu-repo/semantics/altIdentifier/doi/10.1155/2015/120698info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:16:59Zoai:sedici.unlp.edu.ar:10915/85739Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:16:59.406SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
On a conjecture regarding Fisher information |
| title |
On a conjecture regarding Fisher information |
| spellingShingle |
On a conjecture regarding Fisher information Plastino, Ángel Luis Ciencias Exactas Entropy Fisher information Complexity |
| 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 |
| dc.creator.none.fl_str_mv |
Plastino, Ángel Luis Bellomo, Guido Plastino, Ángel Ricardo |
| author |
Plastino, Ángel Luis |
| author_facet |
Plastino, Ángel Luis Bellomo, Guido Plastino, Ángel Ricardo |
| author_role |
author |
| author2 |
Bellomo, Guido Plastino, Ángel Ricardo |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Ciencias Exactas Entropy Fisher information Complexity |
| topic |
Ciencias Exactas Entropy Fisher information Complexity |
| dc.description.none.fl_txt_mv |
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 → ∞. Facultad de Ciencias Exactas Instituto de Física La Plata |
| 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 → ∞. |
| publishDate |
2015 |
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2015 |
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eng |
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