Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions

Li Gao; Marius Junge; Nicolas LaRacuente

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Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions

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arxiv 1807.08838 v1 pith:ACY3HH6J submitted 2018-07-23 math.FA cs.ITmath.ITquant-ph

Li Gao , Marius Junge , Nicolas LaRacuente This is my paper

classification math.FAcs.ITmath.ITquant-ph

keywords inequalityinformationlogarithmicmatrixsobolevalgebraapplicationcompact

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We prove a version of Talagrand's concentration inequality for subordinated sub-Laplacian on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on a finite dimensional matrix algebra the set of self-adjoint generators satisfying a tensor stable modified logarithmic Sobolev inequality is dense.

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