Role of information theoretic uncertainty relations in quantum theory

Petr Jizba*, Jacob A. Dunningham, Jaewoo Joo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)87-114
Number of pages28
JournalAnnals of Physics
Early online date10 Feb 2015
Publication statusPublished - 1 Apr 2015


  • entropy-power inequality
  • information-theoretic uncertainty relation
  • quantum mechanics
  • Rényi entropy


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