Abstract
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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Rumin, M. An Entropic Uncertainty Principle for Positive Operator Valued Measures. Lett Math Phys 100, 291–308 (2012). https://doi.org/10.1007/s11005-011-0543-4
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DOI: https://doi.org/10.1007/s11005-011-0543-4