General Probabilistic Theories with a Gleason-type Theorem

Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We identify the class of general probabilistic theories which a...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Victoria J Wright, Stefan Weigert
Formato:	article
Lenguaje:	EN
Publicado:	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/b8ed8507fdb2434494d706fcb8140c31
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:b8ed8507fdb2434494d706fcb8140c31
record_format	dspace
spelling	oai:doaj.org-article:b8ed8507fdb2434494d706fcb8140c312021-11-25T14:50:32ZGeneral Probabilistic Theories with a Gleason-type Theorem2521-327X10.22331/q-2021-11-25-588https://doaj.org/article/b8ed8507fdb2434494d706fcb8140c312021-11-01T00:00:00Zhttps://quantum-journal.org/papers/q-2021-11-25-588/pdf/https://doaj.org/toc/2521-327XGleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We identify the class of general probabilistic theories which also admit Gleason-type theorems. It contains theories satisfying the no-restriction hypothesis as well as others which can simulate such an unrestricted theory arbitrarily well when allowing for post-selection on measurement outcomes. Our result also implies that the standard no-restriction hypothesis applied to effects is not equivalent to the dual no-restriction hypothesis applied to states which is found to be less restrictive.Victoria J WrightStefan WeigertVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenarticlePhysicsQC1-999ENQuantum, Vol 5, p 588 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Victoria J Wright Stefan Weigert General Probabilistic Theories with a Gleason-type Theorem
description	Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We identify the class of general probabilistic theories which also admit Gleason-type theorems. It contains theories satisfying the no-restriction hypothesis as well as others which can simulate such an unrestricted theory arbitrarily well when allowing for post-selection on measurement outcomes. Our result also implies that the standard no-restriction hypothesis applied to effects is not equivalent to the dual no-restriction hypothesis applied to states which is found to be less restrictive.
format	article
author	Victoria J Wright Stefan Weigert
author_facet	Victoria J Wright Stefan Weigert
author_sort	Victoria J Wright
title	General Probabilistic Theories with a Gleason-type Theorem
title_short	General Probabilistic Theories with a Gleason-type Theorem
title_full	General Probabilistic Theories with a Gleason-type Theorem
title_fullStr	General Probabilistic Theories with a Gleason-type Theorem
title_full_unstemmed	General Probabilistic Theories with a Gleason-type Theorem
title_sort	general probabilistic theories with a gleason-type theorem
publisher	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
publishDate	2021
url	https://doaj.org/article/b8ed8507fdb2434494d706fcb8140c31
work_keys_str_mv	AT victoriajwright generalprobabilistictheorieswithagleasontypetheorem AT stefanweigert generalprobabilistictheorieswithagleasontypetheorem
_version_	1718413402809827328

General Probabilistic Theories with a Gleason-type Theorem

Ejemplares similares