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Symmetric polynomials in information theory: entropy and subentropy

dc.creatorJozsa, Richard
dc.creatorMitchison, Graeme
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.publisherAIP Publishing
dc.publisherJournal of Mathematical Physics
dc.rightsAttribution-NonCommercial 2.0 UK: England & Wales
dc.titleSymmetric polynomials in information theory: entropy and subentropy

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