dc.creator | Jozsa, Richard | |
dc.creator | Mitchison, Graeme | |
dc.date.accessioned | 2018-11-24T23:18:20Z | |
dc.date.available | 2015-08-20T08:55:39Z | |
dc.date.available | 2018-11-24T23:18:20Z | |
dc.date.issued | 2015-06-12 | |
dc.identifier | https://www.repository.cam.ac.uk/handle/1810/250331 | |
dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3257 | |
dc.description.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 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.language | en | |
dc.publisher | AIP Publishing | |
dc.publisher | Journal of Mathematical Physics | |
dc.rights | http://creativecommons.org/licenses/by-nc/2.0/uk/ | |
dc.rights | Attribution-NonCommercial 2.0 UK: England & Wales | |
dc.title | Symmetric polynomials in information theory: entropy and subentropy | |
dc.type | Article | |