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dc.contributor.authorHuber, S.
dc.contributor.authorKönig, R.
dc.contributor.authorVershynina, A.
dc.date.accessioned2016-07-22T21:02:27Z
dc.date.available2016-07-22T21:02:27Z
dc.date.issued2016-07-22
dc.identifier.issn0022-2488
dc.identifier.urihttp://hdl.handle.net/20.500.11824/304
dc.description.abstractWe establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality also gives rise to several related inequalities whose counterparts are well-known in the classical setting: in particular, it implies an entropy power inequality for the mentioned convolution operation as well as the isoperimetric inequality, and establishes concavity of the entropy power along trajectories of the quantum heat diffusion semigroup. As an application, we derive a Log-Sobolev inequality for the quantum Ornstein-Uhlenbeck semigroup, and argue that it implies fast convergence towards the fixed point for a large class of initial states.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleGeometric inequalities from phase space translationsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.arxiv1606.08603
dc.relation.projectIDES/1PE/SEV-2013-0323en_US
dc.relation.projectIDEUS/BERC/BERC.2014-2017en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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