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Role of information theoretic uncertainty relations in quantum theory

journal contribution
posted on 2023-06-08, 20:59 authored by Petr Jizba, Jacob DunninghamJacob Dunningham, Jaewoo Joo
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.

History

Publication status

  • Published

Journal

Annals of Physics

ISSN

0003-4916

Publisher

Elsevier

Volume

355

Page range

87-114

Department affiliated with

  • Physics and Astronomy Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2015-06-04

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