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.