An Entropic Uncertainty Principle for Positive Operator Valued Measures

作者：Rumin Michel^*

来源：Letters in Mathematical Physics, 2012, 100(3): 291-308.

DOI：10.1007/s11005-011-0543-4

• entropy
• POVM
• uncertainty principle
• homogeneous spaces
• log-Sobolev

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.

• 出版日期2012-6