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Title: Role of information theoretic uncertainty relations in quantum theory

Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson–Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson–Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. FNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1 (Czech Republic)
  2. (Germany)
  3. Department of Physics and Astronomy, University of Sussex, Falmer, Brighton, BN1 9QH (United Kingdom)
  4. Advanced Technology Institute and Department of Physics, University of Surrey, Guildford, GU2 7XH (United Kingdom)
Publication Date:
OSTI Identifier:
22451148
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 355; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISTRIBUTION FUNCTIONS; ENERGY LEVELS; ENTROPY; INFORMATION THEORY; QUANTUM MECHANICS; UNCERTAINTY PRINCIPLE