An entropic uncertainty principle for positive operator valued measures

Details An entropic uncertainty principle for positive operator valued measures An entropic uncertainty principle for positive operator valued measures

2011-09-27

arxiv.org/abs/1109.5889v2

Mathematics

Functional Analysis

14 pages. v2: a technical assumption removed in main result

Scientific paper

Extending a recent result by Frank and Lieb, we show an entropic uncertainty
principle for mixed states in a Hilbert space relatively to pairs of positive
operator valued measures that are independent in some sense. This yields
spatial-spectral uncertainty principles and log-Sobolev inequalities for
invariant operators on homogeneous spaces, which are sharp in the compact case.

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