dorsal/arxiv
View SchemaPOVMs and Naimark's theorem without sums
| Authors | Bob Coecke, Eric Oliver Paquette |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608072 |
| URL | https://arxiv.org/abs/quant-ph/0608072 |
Abstract
We provide a definition of POVM in terms of abstract tensor structure only. It is justified in two distinct manners. i. 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 on an extended system, and this proof is moreover purely graphical. ii. Our definition coincides with the usual one for the particular case of the Hilbert space tensor product. We also point to a very useful normal form result for the classical object structure introduced in quant-ph/0608035.
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"abstract": "We provide a definition of POVM in terms of abstract tensor structure only.\nIt is justified in two distinct manners. i. At this abstract level we are still\nable to prove Naimark\u0027s theorem, hence establishing a bijective correspondence\nbetween abstract POVMs and abstract projective measurements on an extended\nsystem, and this proof is moreover purely graphical. ii. Our definition\ncoincides with the usual one for the particular case of the Hilbert space\ntensor product. We also point to a very useful normal form result for the\nclassical object structure introduced in quant-ph/0608035.",
"arxiv_id": "quant-ph/0608072",
"authors": [
"Bob Coecke",
"Eric Oliver Paquette"
],
"categories": [
"quant-ph",
"math-ph",
"math.CT",
"math.MP",
"math.QA"
],
"title": "POVMs and Naimark\u0027s theorem without sums",
"url": "https://arxiv.org/abs/quant-ph/0608072"
},
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