Entropic Uncertainty - Sketch of Proof

Sketch of Proof

The proof of this tight inequality depends on the so-called (q, p)-norm of the Fourier transformation. (Establishing this norm is the most difficult part of the proof.) From this norm we are able to establish a lower bound on the sum of the (differential) Rényi entropies where For simplicity, we consider this inequality only in one dimension; the extension to multiple dimensions is straightforward and can be found in the literature cited.