| Форма представления | Статьи в зарубежных журналах и сборниках |
| Год публикации | 2024 |
| Язык | английский |
|
Бикчентаев Айрат Мидхатович, автор
|
|
Амосов Григорий Геннадьевич, автор
Сакбаев Всеволод Жанович, автор
|
| Библиографическое описание на языке оригинала |
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 |
| Аннотация |
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. |
| Ключевые слова |
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 |
| Название журнала |
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
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| Ссылка для РПД |
http://dspace.kpfu.ru/xmlui/bitstream/handle/net/184103/F_Psim004.pdf?sequence=1&isAllowed=y
|
| Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку |
https://repository.kpfu.ru/?p_id=300182 |
| Файлы ресурса | |
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Полная запись метаданных  |
| Поле DC |
Значение |
Язык |
| dc.contributor.author |
Бикчентаев Айрат Мидхатович |
ru_RU |
| dc.contributor.author |
Амосов Григорий Геннадьевич |
ru_RU |
| dc.contributor.author |
Сакбаев Всеволод Жанович |
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/?p_id=300182 |
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 |
Статьи в зарубежных журналах и сборниках |
ru_RU |
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