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Title: α-z-Rényi relative entropies

We consider a two-parameter family of Rényi relative entropies D{sub α,z}(ρ ∥ σ) that are quantum generalisations of the classical Rényi divergence D{sub α}(p ∥ q). This family includes many known relative entropies (or divergences) such as the quantum relative entropy, the recently defined quantum Rényi divergences, as well as the quantum Rényi relative entropies. All its members satisfy the quantum generalizations of Rényi’s axioms for a divergence. We consider the range of the parameters α, z for which the data-processing inequality holds. We also investigate a variety of limiting cases for the two parameters, obtaining explicit formulas for each one of them.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Mathematics, Royal Holloway University of London, Egham TW20 0EX (United Kingdom)
  2. (Belgium)
  3. Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB (United Kingdom)
Publication Date:
OSTI Identifier:
22403101
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 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; DATA PROCESSING; ENERGY QUALITY; ENTROPY; QUANTUM MECHANICS