KFU. Card publication. EXTREME POINT OF COMPLETELY CONVEX STATE STRUCTURE

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FEDERAL UNIVERSITY

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EXTREME POINT OF COMPLETELY CONVEX STATE STRUCTURE

Form of presentation

Articles in international journals and collections

Year of publication

2024

Язык

английский

Authors, employees of KFU

Khaliullin Samigulla Garifullovich, author

Bibliographic description in the original language

Khaliullin S.G., EXTREME POINT OF COMPLETELY CONVEX STATE STRUCTURE//Ufa Mathematical Journal. - 2024. - Vol.16, Is.3. - P.107-112.

Annotation

It is well–known that the set of states of a given quantum mechanical system is to be closed from the point of view of the operational approach if we want to make mixed states or convex combinations. That is, s1 and s2 are states, then the same is to be true for λs1 + (1 − λ)s2, where 0 < λ < 1. We can deﬁne a convex combination of elements in a linear space, but unfortunately, in the general case the linear space is artiﬁcial for the set of states and has no physical meaning, but the procedure of forming the mixtures of states has a natural meaning. This is why we provide an abstract deﬁnition of the mixtures, which is independent of the linearity notion. We call this space a convex structure. In the work we consider state spaces, generalized state spaces, in which we select pure states, deﬁne operations and eﬀects associated with the operations. We also consider ultraproducts of the sequences of these structures, operations and eﬀects.

Keywords

generalized states, convex states, operation, ultraproducts

The name of the journal

Ufa Mathematical Journal

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85208757447&doi=10.13108%2f2024-16-3-107&partnerID=40&md5=20bb4bc5642e18bc9058ae89988e68f5

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=307641&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Khaliullin Samigulla Garifullovich	ru_RU
dc.date.accessioned	2024-01-01T00:00:00Z	ru_RU
dc.date.available	2024-01-01T00:00:00Z	ru_RU
dc.date.issued	2024	ru_RU
dc.identifier.citation	Khaliullin S.G., EXTREME POINT OF COMPLETELY CONVEX STATE STRUCTURE//Ufa Mathematical Journal. - 2024. - Vol.16, Is.3. - P.107-112.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=307641&p_lang=2	ru_RU
dc.description.abstract	Ufa Mathematical Journal	ru_RU
dc.description.abstract	It is well–known that the set of states of a given quantum mechanical system is to be closed from the point of view of the operational approach if we want to make mixed states or convex combinations. That is, s1 and s2 are states, then the same is to be true for λs1 + (1 − λ)s2, where 0 < λ < 1. We can deﬁne a convex combination of elements in a linear space, but unfortunately, in the general case the linear space is artiﬁcial for the set of states and has no physical meaning, but the procedure of forming the mixtures of states has a natural meaning. This is why we provide an abstract deﬁnition of the mixtures, which is independent of the linearity notion. We call this space a convex structure. In the work we consider state spaces, generalized state spaces, in which we select pure states, deﬁne operations and eﬀects associated with the operations. We also consider ultraproducts of the sequences of these structures, operations and eﬀects.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	generalized states	ru_RU
dc.subject	convex states	ru_RU
dc.subject	operation	ru_RU
dc.subject	ultraproducts	ru_RU
dc.title	EXTREME POINT OF COMPLETELY CONVEX STATE STRUCTURE	ru_RU
dc.type	Articles in international journals and collections	ru_RU