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.

Read more about this topic:  Entropic Uncertainty

Famous quotes containing the words sketch and/or proof:

    the vagabond began
    To sketch a face that well might buy the soul of any man.
    Then, as he placed another lock upon the shapely head,
    With a fearful shriek, he leaped and fell across the
    picture—dead.
    Hugh Antoine D’Arcy (1843–1925)

    The thing with Catholicism, the same as all religions, is that it teaches what should be, which seems rather incorrect. This is “what should be.” Now, if you’re taught to live up to a “what should be” that never existed—only an occult superstition, no proof of this “should be”Mthen you can sit on a jury and indict easily, you can cast the first stone, you can burn Adolf Eichmann, like that!
    Lenny Bruce (1925–1966)