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Conference Paper: On quantum estimation, quantum cloning and finite quantum de Finetti theorems

TitleOn quantum estimation, quantum cloning and finite quantum de Finetti theorems
Authors
Issue Date2011
Citation
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2011, v. 6519 LNCS, p. 9-25 How to Cite?
AbstractThis paper presents a series of results on the interplay between quantum estimation, cloning and finite de Finetti theorems. First, we consider the measure-and-prepare channel that uses optimal estimation to convert M copies into k approximate copies of an unknown pure state and we show that this channel is equal to a random loss of all but s particles followed by cloning from s to k copies. When the number k of output copies is large with respect to the number M of input copies the measure-and-prepare channel converges in diamond norm to the optimal universal cloning. In the opposite case, when M is large compared to k, the estimation becomes almost perfect and the measure-and-prepare channel converges in diamond norm to the partial trace over all but k systems. This result is then used to derive de Finetti-type results for quantum states and for symmetric broadcast channels, that is, channels that distribute quantum information to many receivers in a permutationally invariant fashion. Applications of the finite de Finetti theorem for symmetric broadcast channels include the derivation of diamond-norm bounds on the asymptotic convergence of quantum cloning to state estimation and the derivation of bounds on the amount of quantum information that can be jointly decoded by a group of k receivers at the output of a symmetric broadcast channel. © 2011 Springer-Verlag.
Persistent Identifierhttp://hdl.handle.net/10722/213145
ISSN
2005 Impact Factor: 0.402
2015 SCImago Journal Rankings: 0.252

 

DC FieldValueLanguage
dc.contributor.authorChiribella, Giulio-
dc.date.accessioned2015-07-28T04:06:17Z-
dc.date.available2015-07-28T04:06:17Z-
dc.date.issued2011-
dc.identifier.citationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2011, v. 6519 LNCS, p. 9-25-
dc.identifier.issn0302-9743-
dc.identifier.urihttp://hdl.handle.net/10722/213145-
dc.description.abstractThis paper presents a series of results on the interplay between quantum estimation, cloning and finite de Finetti theorems. First, we consider the measure-and-prepare channel that uses optimal estimation to convert M copies into k approximate copies of an unknown pure state and we show that this channel is equal to a random loss of all but s particles followed by cloning from s to k copies. When the number k of output copies is large with respect to the number M of input copies the measure-and-prepare channel converges in diamond norm to the optimal universal cloning. In the opposite case, when M is large compared to k, the estimation becomes almost perfect and the measure-and-prepare channel converges in diamond norm to the partial trace over all but k systems. This result is then used to derive de Finetti-type results for quantum states and for symmetric broadcast channels, that is, channels that distribute quantum information to many receivers in a permutationally invariant fashion. Applications of the finite de Finetti theorem for symmetric broadcast channels include the derivation of diamond-norm bounds on the asymptotic convergence of quantum cloning to state estimation and the derivation of bounds on the amount of quantum information that can be jointly decoded by a group of k receivers at the output of a symmetric broadcast channel. © 2011 Springer-Verlag.-
dc.languageeng-
dc.relation.ispartofLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)-
dc.titleOn quantum estimation, quantum cloning and finite quantum de Finetti theorems-
dc.typeConference_Paper-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1007/978-3-642-18073-6_2-
dc.identifier.scopuseid_2-s2.0-79251547376-
dc.identifier.volume6519 LNCS-
dc.identifier.spage9-
dc.identifier.epage25-
dc.identifier.eissn1611-3349-

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