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20 April 2024

» arxiv » quant-ph/0608072

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POVMs and Naimark's theorem without sums
Bob Coecke ; Eric Oliver Paquette ; quant-ph/0402130 ; quant-ph/0510032 ; quant-ph/0608035 ; PostScript ; PDF ; Other formats ;
Date:	8 Aug 2006
Abstract:	We introduce POVMs within the purely graphical categorical quantum mechanical formalism in terms of dagger-compact categories (cf. quant-ph/0402130, quant-ph/0510032 & quant-ph/0608035). Our definition is justified by two facts: i. We provide a counterpart to Naimark’s theorem, which establishes a bijective correspondence between POVMs and abstract projective measurements on an extended system; ii. In the category of Hilbert spaces and linear maps our definition coincides with the usual one.
Source:	arXiv, quant-ph/0608072
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