Entropic uncertainty relations in quantum mechanics. (English) Zbl 0584.94009

Bialynicki-Birula, Iwo

Quantum probability and applications II, Proc. 2nd Workshop, Heidelberg/Ger. 1984, Lect. Notes Math. 1136, 90-103 (1985).

[For the entire collection see Zbl 0566.00017.]
The standard uncertainty principle \(\Delta A\cdot \Delta B\geq | <C>| /2\) \((C=AB-BA)\) is based on the dispersion \(\Delta\) measuring the spread of a physical quantity around its mean value. The pleasantly readable paper popularizes the application of the Shannon entropy to measure this spread, an idea due to D. Deutsch. The author deduces new lower bounds for \(H^ A+H^ B\) using his joint work with J. Mycielski [Commun. Math. Phys. 44, 129-132 (1975)] when (A,B) is the position-momentum and the angle-angular momentum pair.

Reviewer: D.Petz

MSC:

94A17	Measures of information, entropy
81S99	General quantum mechanics and problems of quantization

Keywords:

quantum measurement; uncertainty; Shannon entropy