dc.contributor.author
Boes, Paul
dc.contributor.author
Ng, Nelly H. Y.
dc.contributor.author
Wilming, Henrik
dc.date.accessioned
2022-04-08T10:37:31Z
dc.date.available
2022-04-08T10:37:31Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/34651
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-34369
dc.description.abstract
The variance of (relative) surprisal, also known as varentropy, so far mostly plays a role in information theory as quantifying the leading-order corrections to asymptotic independent and identically distributed (IID) limits. Here, we comprehensively study the use of it to derive single-shot results in (quantum) information theory. We show that it gives genuine sufficient and necessary conditions for approximate state transitions between pairs of quantum states in the single-shot setting, without the need for further optimization. We also clarify its relation to smoothed min and max entropies, and construct a monotone for resource theories using only the standard (relative) entropy and variance of (relative) surprisal. This immediately gives rise to enhanced lower bounds for entropy production in random processes. We establish certain properties of the variance of relative surprisal, which will be useful for further investigations, such as uniform continuity and upper bounds on the violation of subadditivity. Motivated by our results, we further derive a simple and physically appealing axiomatic single-shot characterization of (relative) entropy, which we believe to be of independent interest. We illustrate our results with several applications, ranging from interconvertibility of ergodic states, over Landauer erasure to a bound on the necessary dimension of the catalyst for catalytic state transitions and Boltzmann’s H theorem.
en
dc.format.extent
31 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Quantum information processing
en
dc.subject
Quantum thermodynamics
en
dc.subject
Resource theories
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::530 Physik::530 Physik
dc.title
Variance of Relative Surprisal as Single-Shot Quantifier
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.articlenumber
010325
dcterms.bibliographicCitation.doi
10.1103/PRXQuantum.3.010325
dcterms.bibliographicCitation.journaltitle
PRX Quantum
dcterms.bibliographicCitation.number
1
dcterms.bibliographicCitation.volume
3
dcterms.bibliographicCitation.url
https://doi.org/10.1103/PRXQuantum.3.010325
refubium.affiliation
Physik
refubium.affiliation.other
Dahlem Center für komplexe Quantensysteme
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
2691-3399
refubium.resourceType.provider
WoS-Alert