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Article: Normal completely positive maps on the space of quantum operations

TitleNormal completely positive maps on the space of quantum operations
Authors
Issue Date2013
Citation
Open Systems and Information Dynamics, 2013, v. 20, n. 1 How to Cite?
AbstractQuantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite-dimensional setting, to the case of higher-order maps transforming quantum operations with input in a separable von Neumann algebra and output in the algebra of the bounded operators on a given separable Hilbert space. In this setting we prove two dilation theorems for quantum supermaps that are the analogues of the Stinespring and Radon-Nikodym theorems for quantum operations. Finally, we consider the case of quantum superinstruments, namely measures with values in the set of quantum supermaps, and derive a dilation theorem for them that is analogue to Ozawa's theorem for quantum instruments. The three dilation theorems presented here show that all the supermaps defined in this paper can be implemented by connecting devices in quantum circuits. © 2013 World Scientific Publishing Company.
Persistent Identifierhttp://hdl.handle.net/10722/213296
ISSN
2015 Impact Factor: 1.306
2015 SCImago Journal Rankings: 0.549
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChiribella, Giulio-
dc.contributor.authorToigo, Alessandro-
dc.contributor.authorUmanità, Veronica-
dc.date.accessioned2015-07-28T04:06:48Z-
dc.date.available2015-07-28T04:06:48Z-
dc.date.issued2013-
dc.identifier.citationOpen Systems and Information Dynamics, 2013, v. 20, n. 1-
dc.identifier.issn1230-1612-
dc.identifier.urihttp://hdl.handle.net/10722/213296-
dc.description.abstractQuantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite-dimensional setting, to the case of higher-order maps transforming quantum operations with input in a separable von Neumann algebra and output in the algebra of the bounded operators on a given separable Hilbert space. In this setting we prove two dilation theorems for quantum supermaps that are the analogues of the Stinespring and Radon-Nikodym theorems for quantum operations. Finally, we consider the case of quantum superinstruments, namely measures with values in the set of quantum supermaps, and derive a dilation theorem for them that is analogue to Ozawa's theorem for quantum instruments. The three dilation theorems presented here show that all the supermaps defined in this paper can be implemented by connecting devices in quantum circuits. © 2013 World Scientific Publishing Company.-
dc.languageeng-
dc.relation.ispartofOpen Systems and Information Dynamics-
dc.titleNormal completely positive maps on the space of quantum operations-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1142/S1230161213500030-
dc.identifier.scopuseid_2-s2.0-84875042189-
dc.identifier.volume20-
dc.identifier.issue1-
dc.identifier.isiWOS:000316950000003-

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