Three qubit entanglement within graphical Z/X-calculus
The compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quantum entanglement. In particular the graphical calculus of complementary observables and corresponding phases due to Duncan and one of the authors is used to construct representative members of the two ge...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2011-03-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1103.2811v1 |
| _version_ | 1818917471486214144 |
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| author | Bob Coecke Bill Edwards |
| author_facet | Bob Coecke Bill Edwards |
| author_sort | Bob Coecke |
| collection | DOAJ |
| description | The compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quantum entanglement. In particular the graphical calculus of complementary observables and corresponding phases due to Duncan and one of the authors is used to construct representative members of the two genuinely tripartite SLOCC classes of 3-qubit entangled states, GHZ and W. This nicely illustrates the respectively pairwise and global tripartite entanglement found in the W- and GHZ-class states. A new concept of supplementarity allows us to characterise inhabitants of the W class within the abstract diagrammatic calculus; these method extends to more general multipartite qubit states. |
| first_indexed | 2024-12-20T00:34:36Z |
| format | Article |
| id | doaj.art-16dc6cee25744b8fa4fc9d640d047cc9 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-20T00:34:36Z |
| publishDate | 2011-03-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-16dc6cee25744b8fa4fc9d640d047cc92022-12-21T19:59:48ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802011-03-0152Proc. HPC 2010223310.4204/EPTCS.52.3Three qubit entanglement within graphical Z/X-calculusBob CoeckeBill EdwardsThe compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quantum entanglement. In particular the graphical calculus of complementary observables and corresponding phases due to Duncan and one of the authors is used to construct representative members of the two genuinely tripartite SLOCC classes of 3-qubit entangled states, GHZ and W. This nicely illustrates the respectively pairwise and global tripartite entanglement found in the W- and GHZ-class states. A new concept of supplementarity allows us to characterise inhabitants of the W class within the abstract diagrammatic calculus; these method extends to more general multipartite qubit states.http://arxiv.org/pdf/1103.2811v1 |
| spellingShingle | Bob Coecke Bill Edwards Three qubit entanglement within graphical Z/X-calculus Electronic Proceedings in Theoretical Computer Science |
| title | Three qubit entanglement within graphical Z/X-calculus |
| title_full | Three qubit entanglement within graphical Z/X-calculus |
| title_fullStr | Three qubit entanglement within graphical Z/X-calculus |
| title_full_unstemmed | Three qubit entanglement within graphical Z/X-calculus |
| title_short | Three qubit entanglement within graphical Z/X-calculus |
| title_sort | three qubit entanglement within graphical z x calculus |
| url | http://arxiv.org/pdf/1103.2811v1 |
| work_keys_str_mv | AT bobcoecke threequbitentanglementwithingraphicalzxcalculus AT billedwards threequbitentanglementwithingraphicalzxcalculus |