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- W1500705441 abstract "Entropy 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 significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials we also derive a series of further properties of H and Q." @default.
- W1500705441 created "2016-06-24" @default.
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- W1500705441 date "2014-04-30" @default.
- W1500705441 modified "2023-09-27" @default.
- W1500705441 title "Symmetric polynomials in information theory: entropy and subentropy" @default.
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- W1500705441 hasPublicationYear "2014" @default.
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