KFU. Card publication. On the extreme points of sets in spaces of operators and spaces of states

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FEDERAL UNIVERSITY

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ON THE EXTREME POINTS OF SETS IN SPACES OF OPERATORS AND SPACES OF STATES

Form of presentation

Articles in international journals and collections

Year of publication

2024

Язык

английский

Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Other authors

Amosov Grigoriy Gennadevich, author

Sakbaev Vsevolod Zhanovich, author

Bibliographic description in the original language

G.G. Amosov, A.M. Bikchentaev, V. Zh. Sakbaev, On Extreme Points of Sets in Operator Spaces and State Spaces, Proc. Steklov Inst. Math., 324 (2024), 4--17

Annotation

A representation of the set of quantum states by barycenters of non-negative normalized finite additive measures on a unit sphere of Hilbert space H is obtained. In terms of the properties of a measure on a unit sphere of space H, the conditions for its barycenter to belong to the set of extreme points of the set of quantum states and to the set of normal states are derived. A characterization of the unitary elements of the unital C∗-algebra in terms of extreme points is obtained. The extreme points of the unit ball E1 of the normalized ideal space of operators ⟨E,∥⋅∥E⟩ on H are investigated. If U∈extr(E1) for some unitary operator U∈B(H), then V∈extr(E1) for all unitary operators V∈B(H). Quantum correlations corresponding to the singular state on the algebra of all bounded operators in a Hilbert space are constructed.

Keywords

Hilbert space, linear operator, C*-algebra, von Neumann algebra, normed ideal space of operators, quantum state, finite-additive measure, baricenter, extemal point, quantum korrelations, generated by states

The name of the journal

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS

On-line resource for training course

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/184103/F_Psim004.pdf?sequence=1&isAllowed=y

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

https://repository.kpfu.ru/eng/?p_id=300182&p_lang=2

Resource files

File name	Size (MB)	Format
F_Psim004.pdf	1,64	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.contributor.author	Amosov Grigoriy Gennadevich	ru_RU
dc.contributor.author	Sakbaev Vsevolod Zhanovich	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	G.G. Amosov, A.M. Bikchentaev, V. Zh. Sakbaev, On Extreme Points of Sets in Operator Spaces and State Spaces, Proc. Steklov Inst. Math., 324 (2024), 4--17	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=300182&p_lang=2	ru_RU
dc.description.abstract	PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS	ru_RU
dc.description.abstract	A representation of the set of quantum states by barycenters of non-negative normalized finite additive measures on a unit sphere of Hilbert space H is obtained. In terms of the properties of a measure on a unit sphere of space H, the conditions for its barycenter to belong to the set of extreme points of the set of quantum states and to the set of normal states are derived. A characterization of the unitary elements of the unital C∗-algebra in terms of extreme points is obtained. The extreme points of the unit ball E1 of the normalized ideal space of operators ⟨E,∥⋅∥E⟩ on H are investigated. If U∈extr(E1) for some unitary operator U∈B(H), then V∈extr(E1) for all unitary operators V∈B(H). Quantum correlations corresponding to the singular state on the algebra of all bounded operators in a Hilbert space are constructed.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hilbert space	ru_RU
dc.subject	linear operator	ru_RU
dc.subject	C*-algebra	ru_RU
dc.subject	von Neumann algebra	ru_RU
dc.subject	normed ideal space of operators	ru_RU
dc.subject	quantum state	ru_RU
dc.subject	finite-additive measure	ru_RU
dc.subject	baricenter	ru_RU
dc.subject	extemal point	ru_RU
dc.subject	quantum korrelations	ru_RU
dc.subject	generated by states	ru_RU
dc.title	On the extreme points of sets in spaces of operators and spaces of states	ru_RU
dc.type	Articles in international journals and collections	ru_RU