Role of information theoretic uncertainty relations in quantum theory

Jizba, Petr, Dunningham, Jacob A and Joo, Jaewoo (2015) Role of information theoretic uncertainty relations in quantum theory. Annals of Physics, 355. pp. 87-114. ISSN 0003-4916

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Subjects: Q Science > QC Physics
Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics
Depositing User: Jacob Dunningham
Date Deposited: 04 Jun 2015 15:20
Last Modified: 04 Jun 2015 15:20
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