Min-Entropic Quantities Induced by Cones: Properties & Operational Interpretations

Ian George, Eric Chitambar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In one-shot and zero-error information theory, the conditional min-entropy is a fundamental tool. It may be expressed as a conic program over the positive semidefinite cone. Recently, Chitambar et al. showed that the same conic program altered to be over the separable cone is a measure of transmitting classical communication over a quantum channel called the 'communication value.' In this work, we extend this idea to a broad class of convex cones to induce new families of entropic quantities. We show this methodology has operational relevance by characterizing a generalized notion of communication value and relating a class of cone-restricted entropies to a partial ordering on converting quantum channels via bistochastic preprocessing. We also show regularized smooth versions of these entropic quantities do not in general converge to the von Neumann entropy, which shows tasks characterized by these quantities are not equivalent even in an asymptotic i.i.d. fashion.

Original languageEnglish (US)
Title of host publication2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1005-1010
Number of pages6
ISBN (Electronic)9798350382846
DOIs
StatePublished - 2024
Event2024 IEEE International Symposium on Information Theory, ISIT 2024 - Athens, Greece
Duration: Jul 7 2024Jul 12 2024

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2024 IEEE International Symposium on Information Theory, ISIT 2024
Country/TerritoryGreece
CityAthens
Period7/7/247/12/24

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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