Mathematical Physics Seminar
Quantum analogues of geometric inequalities for Information Theory
Location: Hill 705
Date & time: Thursday, 26 January 2017 at 12:00PM - 12:11PM
Anna Vershynina, BCAM-Basque Center for Applied Mathematics, Spain: Geometric inequalities, such as entropy power inequality or theisoperimetric inequality, relate geometric quantities, such as volumesand surface areas. Classically, these inequalities have usefulapplications for obtaining bounds on channel capacities, and derivinglog-Sobolev inequalities. In my talk I provide quantum analogues ofcertain well-known inequalities from classical Information Theory,with the most notable being the isoperimetric inequality forentropies. The latter inequality is useful for the study ofconvergence of certain semigroups to fixed points. In the talkdemonstrate how to apply the isoperimetric inequality for entropies toshow exponentially fast convergence of quantum Ornstein-Uhlenbeck(qOU) semigroup to a fixed point of the process. The inequalityrepresenting the fast convergence can be viewed as a quantum analogue of a classical Log-Sobolev inequality.