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Title: On quantum Rényi entropies: A new generalization and some properties

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5]
  1. Department of Mathematics, ETH Zurich, 8092 Zürich (Switzerland)
  2. Department of Computer Science, Aarhus University, 8200 Aarhus (Denmark)
  3. Department of Mathematics, Technische Universität München, 85748 Garching (Germany)
  4. CWI (Centrum Wiskunde and Informatica), 1090 Amsterdam (Netherlands)
  5. Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)
Publication Date:
OSTI Identifier:
22251256
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 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; ENTROPY; INFORMATION THEORY