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dc.contributor.authorJozsa, Richarden
dc.contributor.authorMitchison, Graemeen
dc.date.accessioned2015-08-20T08:55:39Z
dc.date.available2015-08-20T08:55:39Z
dc.date.issued2015-06-12en
dc.identifier.citationJournal of Mathematical Physics 56, 062201 (2015); http://dx.doi.org/10.1063/1.4922317en
dc.identifier.issn0022-2488
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/250331
dc.description.abstractEntropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities, and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore we see that H and the intrinsically quantum informational quantity Q become surprisingly closely related in functional form, suggesting a special signi cance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials we also derive a series of further properties of H and Q.
dc.languageEnglishen
dc.language.isoenen
dc.publisherAIP Publishing
dc.rightsAttribution-NonCommercial 2.0 UK: England & Wales*
dc.rights.urihttp://creativecommons.org/licenses/by-nc/2.0/uk/*
dc.titleSymmetric polynomials in information theory: entropy and subentropyen
dc.typeArticle
dc.description.versionThis is the accepted manuscript. The final version is available at http://scitation.aip.org/content/aip/journal/jmp/56/6/10.1063/1.4922317.en
prism.number062201en
prism.publicationDate2015en
prism.publicationNameJournal of Mathematical Physicsen
prism.volume56en
rioxxterms.versionofrecord10.1063/1.4922317en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2015-06-12en
dc.identifier.eissn1089-7658
rioxxterms.typeJournal Article/Reviewen


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Attribution-NonCommercial 2.0 UK: England & Wales
Except where otherwise noted, this item's licence is described as Attribution-NonCommercial 2.0 UK: England & Wales