dc.contributor.author
Boes, P.
dc.contributor.author
Wilming, H.
dc.contributor.author
Gallego, R.
dc.contributor.author
Eisert, J.
dc.date.accessioned
2018-11-08T13:27:00Z
dc.date.available
2018-11-08T13:27:00Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/23193
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-985
dc.description.abstract
Randomness is a defining element of mixing processes in nature and an essential ingredient to many protocols in quantum information. In this work, we investigate how much randomness is required to transform a given quantum state into another one. Specifically, we ask whether there is a gap between the power of a classical source of randomness compared to that of a quantum one. We provide a complete answer to these questions, by identifying provably optimal protocols for both classical and quantum sources of randomness, based on a dephasing construction. We find that in order to implement any noisy transition on a d-dimensional quantum system it is necessary and sufficient to have a quantum source of randomness of dimension √d or a classical one of dimension d. Interestingly, coherences provided by quantum states in a source of randomness offer a quadratic advantage. The process we construct has the additional features to be robust and catalytic; i.e., the source of randomness can be reused. Building upon this formal framework, we illustrate that this dephasing construction can serve as a useful primitive in both equilibration and quantum information theory: We discuss applications describing the smallest measurement device, capturing the smallest equilibrating environment allowed by quantum mechanics, or forming the basis for a cryptographic private quantum channel. We complement the exact analysis with a discussion of approximate protocols based on quantum expanders deriving from discrete Weyl systems. This gives rise to equilibrating environments of remarkably small dimension. Our results highlight the curious feature of randomness that residual correlations and dimension can be traded against each other.
en
dc.format.extent
19 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Quantum Information
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::530 Physik::530 Physik
dc.title
Catalytic Quantum Randomness
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.articlenumber
041016
dcterms.bibliographicCitation.doi
10.1103/PhysRevX.8.041016
dcterms.bibliographicCitation.journaltitle
Physical Review X
dcterms.bibliographicCitation.number
4
dcterms.bibliographicCitation.volume
8
dcterms.bibliographicCitation.url
https://doi.org/10.1103/PhysRevX.8.041016
refubium.affiliation
Physik
refubium.affiliation.other
Institut für Theoretische Physik
refubium.note.author
Der Artikel wurde in einer reinen Open-Access-Zeitschrift publiziert.
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.issn
2160-3308