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Title: Relating different quantum generalizations of the conditional Rényi entropy

Recently a new quantum generalization of the Rényi divergence and the corresponding conditional Rényi entropies was proposed. Here, we report on a surprising relation between conditional Rényi entropies based on this new generalization and conditional Rényi entropies based on the quantum relative Rényi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Rényi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Rényi entropies and derive a new entropic uncertainty relation.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [1] ;  [5]
  1. Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)
  2. (Australia)
  3. Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125 (United States)
  4. (Switzerland)
  5. (Japan)
Publication Date:
OSTI Identifier:
22306091
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENTROPY; PROBABILITY; PURE STATES; QUANTUM MECHANICS; UNCERTAINTY PRINCIPLE