A Complete Set of Invariants for LU-Equivalence of Density Operators
We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This implicitly gives a finite complete set of invariants for local unit...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2017 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148619 |
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| Цитувати: | A Complete Set of Invariants for LU-Equivalence of Density Operators / J. Turner, J. Morton // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 52 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1486192019-02-19T01:25:38Z A Complete Set of Invariants for LU-Equivalence of Density Operators Turner, J. Morton, J. We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This implicitly gives a finite complete set of invariants for local unitary equivalence. This is done by showing that local unitary equivalence of density operators is equivalent to local GL equivalence and then using techniques from algebraic geometry and geometric invariant theory. We also classify the SLOCC polynomial invariants and give a degree bound for generators of the invariant ring in the case of n-qubit pure states. Of course it is well known that polynomial invariants are not a complete set of invariants for SLOCC. 2017 Article A Complete Set of Invariants for LU-Equivalence of Density Operators / J. Turner, J. Morton // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 52 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20G05; 20G45; 81R05; 20C35; 22E70 DOI:10.3842/SIGMA.2017.028 http://dspace.nbuv.gov.ua/handle/123456789/148619 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This implicitly gives a finite complete set of invariants for local unitary equivalence. This is done by showing that local unitary equivalence of density operators is equivalent to local GL equivalence and then using techniques from algebraic geometry and geometric invariant theory. We also classify the SLOCC polynomial invariants and give a degree bound for generators of the invariant ring in the case of n-qubit pure states. Of course it is well known that polynomial invariants are not a complete set of invariants for SLOCC. |
| format |
Article |
| author |
Turner, J. Morton, J. |
| spellingShingle |
Turner, J. Morton, J. A Complete Set of Invariants for LU-Equivalence of Density Operators Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Turner, J. Morton, J. |
| author_sort |
Turner, J. |
| title |
A Complete Set of Invariants for LU-Equivalence of Density Operators |
| title_short |
A Complete Set of Invariants for LU-Equivalence of Density Operators |
| title_full |
A Complete Set of Invariants for LU-Equivalence of Density Operators |
| title_fullStr |
A Complete Set of Invariants for LU-Equivalence of Density Operators |
| title_full_unstemmed |
A Complete Set of Invariants for LU-Equivalence of Density Operators |
| title_sort |
complete set of invariants for lu-equivalence of density operators |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148619 |
| citation_txt |
A Complete Set of Invariants for LU-Equivalence of Density Operators / J. Turner, J. Morton // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 52 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:30:15Z |
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2023-05-20T17:30:15Z |
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