POVMs and Naimark's theorem without sums
We provide a definition of POVM in terms of abstract <em>tensor structure</em> only. It is justified in two distinct manners. <strong>i</strong>. At this abstract level we are still able to prove Naimark's theorem, hence establishing a bijective correspondence between ab...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2008
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| _version_ | 1826258728445280256 |
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| author | Coecke, B Paquette, É |
| author_facet | Coecke, B Paquette, É |
| author_sort | Coecke, B |
| collection | OXFORD |
| description | We provide a definition of POVM in terms of abstract <em>tensor structure</em> only. It is justified in two distinct manners. <strong>i</strong>. At this abstract level we are still able to prove Naimark's theorem, hence establishing a bijective correspondence between abstract POVMs and abstract projective measurements (cf. [B. Coecke and D. Pavlovic (2007) <em>Quantum measurements without sums. </em>In: Mathematics of Quantum Computing and Technology. Chapman & Hall, pp. 559–596. E-print available from http://www.arxiv.org/abs//quant-ph/0608035]) on an extended system, and this proof is moreover purely graphical. <strong>ii</strong>. Our definition coincides with the usual one for the particular case of the Hilbert space tensor product. We also provide a very useful <em>normal form</em> result for the classical object structure introduced in [B. Coecke and D. Pavlovic (2007) <em>Quantum measurements without sums.</em> In: Mathematics of Quantum Computing and Technology. Chapman & Hall, pp. 559–596. E-print available from http://www.arxiv.org/abs//quant-ph/0608035]. |
| first_indexed | 2024-03-06T18:38:34Z |
| format | Journal article |
| id | oxford-uuid:0c204112-b5af-476c-8462-453d9df8a8dc |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:38:34Z |
| publishDate | 2008 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:0c204112-b5af-476c-8462-453d9df8a8dc2022-03-26T09:33:12ZPOVMs and Naimark's theorem without sumsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0c204112-b5af-476c-8462-453d9df8a8dcComputer science (mathematics)EnglishOxford University Research Archive - ValetElsevier2008Coecke, BPaquette, ÉWe provide a definition of POVM in terms of abstract <em>tensor structure</em> only. It is justified in two distinct manners. <strong>i</strong>. At this abstract level we are still able to prove Naimark's theorem, hence establishing a bijective correspondence between abstract POVMs and abstract projective measurements (cf. [B. Coecke and D. Pavlovic (2007) <em>Quantum measurements without sums. </em>In: Mathematics of Quantum Computing and Technology. Chapman & Hall, pp. 559–596. E-print available from http://www.arxiv.org/abs//quant-ph/0608035]) on an extended system, and this proof is moreover purely graphical. <strong>ii</strong>. Our definition coincides with the usual one for the particular case of the Hilbert space tensor product. We also provide a very useful <em>normal form</em> result for the classical object structure introduced in [B. Coecke and D. Pavlovic (2007) <em>Quantum measurements without sums.</em> In: Mathematics of Quantum Computing and Technology. Chapman & Hall, pp. 559–596. E-print available from http://www.arxiv.org/abs//quant-ph/0608035]. |
| spellingShingle | Computer science (mathematics) Coecke, B Paquette, É POVMs and Naimark's theorem without sums |
| title | POVMs and Naimark's theorem without sums |
| title_full | POVMs and Naimark's theorem without sums |
| title_fullStr | POVMs and Naimark's theorem without sums |
| title_full_unstemmed | POVMs and Naimark's theorem without sums |
| title_short | POVMs and Naimark's theorem without sums |
| title_sort | povms and naimark s theorem without sums |
| topic | Computer science (mathematics) |
| work_keys_str_mv | AT coeckeb povmsandnaimarkstheoremwithoutsums AT paquettee povmsandnaimarkstheoremwithoutsums |