Cari colleghi,
vi annuncio che martedì 8 novembre, alle ore 15 precise, nell'aula Beltrami del Dipartimento di Matematica dell'Universita' di Pavia,
il Dott. Cambyse Rouzé
(University of Cambridge) terrà un seminario dal titolo
Convergence properties of a quantum diff usion semigroup via
concavity of the quantum entropy power
di cui segue il sunto.
Distinti saluti,
Raffaella Carbone
Abstract
The entropy power, rst de ned by Shannon in his seminal paper, lead to many celebrated
results in information theory and probability theory. In 1985, Costa proved that the entropy
power of a random variable with added Gaussian noise of linearly increasing variance
is concave with respect to . The proof of this result was later simpli ed by Dembo by an
argument based on the so-called Blachman-Stam inequality. This result (and the intermediate
steps of its proof) led to many applications ranging from contractivity properties of certain
Markov semigroups to entropic versions of the Central limit theorem. In this talk I will
discuss a recent analogue of this result proved in the context of quantum harmonic analysis
on phase space. I will then use this result to bound the time of convergence in relative entropy
of a state evolving under a quantum analogue of the heat semigroup. This is joint work with
Dr. Nilanjana Datta and Dr. Yan Pautrat.