Quantum Entanglement and Projective Ring Geometry
The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal quantum entanglement in such systems, we demonstrate that the 1...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2006 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146101 |
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| Цитувати: | Quantum Entanglement and Projective Ring Geometry / M. Planat, M. Saniga, M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 33 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1461012019-02-08T01:23:30Z Quantum Entanglement and Projective Ring Geometry Planat, M. Saniga, M. Kibler, M.R. The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal quantum entanglement in such systems, we demonstrate that the 15 × 15 multiplication table of the associated four-dimensional matrices exhibits a so-far-unnoticed geometrical structure that can be regarded as three pencils of lines in the projective plane of order two. In one of the pencils, which we call the kernel, the observables on two lines share a base of Bell states. In the complement of the kernel, the eight vertices/observables are joined by twelve lines which form the edges of a cube. A substantial part of the paper is devoted to showing that the nature of this geometry has much to do with the structure of the projective lines defined over the rings that are the direct product of n copies of the Galois field GF(2), with n = 2, 3 and 4. 2006 Article Quantum Entanglement and Projective Ring Geometry / M. Planat, M. Saniga, M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 33 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81P15; 51C05; 13M05; 13A15; 51N15; 81R05 http://dspace.nbuv.gov.ua/handle/123456789/146101 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 |
The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal quantum entanglement in such systems, we demonstrate that the 15 × 15 multiplication table of the associated four-dimensional matrices exhibits a so-far-unnoticed geometrical structure that can be regarded as three pencils of lines in the projective plane of order two. In one of the pencils, which we call the kernel, the observables on two lines share a base of Bell states. In the complement of the kernel, the eight vertices/observables are joined by twelve lines which form the edges of a cube. A substantial part of the paper is devoted to showing that the nature of this geometry has much to do with the structure of the projective lines defined over the rings that are the direct product of n copies of the Galois field GF(2), with n = 2, 3 and 4. |
| format |
Article |
| author |
Planat, M. Saniga, M. Kibler, M.R. |
| spellingShingle |
Planat, M. Saniga, M. Kibler, M.R. Quantum Entanglement and Projective Ring Geometry Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Planat, M. Saniga, M. Kibler, M.R. |
| author_sort |
Planat, M. |
| title |
Quantum Entanglement and Projective Ring Geometry |
| title_short |
Quantum Entanglement and Projective Ring Geometry |
| title_full |
Quantum Entanglement and Projective Ring Geometry |
| title_fullStr |
Quantum Entanglement and Projective Ring Geometry |
| title_full_unstemmed |
Quantum Entanglement and Projective Ring Geometry |
| title_sort |
quantum entanglement and projective ring geometry |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146101 |
| citation_txt |
Quantum Entanglement and Projective Ring Geometry / M. Planat, M. Saniga, M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 33 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT planatm quantumentanglementandprojectiveringgeometry AT sanigam quantumentanglementandprojectiveringgeometry AT kiblermr quantumentanglementandprojectiveringgeometry |
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2023-05-20T17:23:49Z |
| last_indexed |
2023-05-20T17:23:49Z |
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1796153200965844992 |