Observability in Quantum Dynamics: an Optimal Transport Approach (in collaboration with Thierry Paul)

Observability refers to the possibility of reconstructing the solution of an evolution PDE from knowing its restriction to some spatial subdomain and on some finite time interval. This is a property dual to controllability, and Bardos-Lebeau and Rauch have given a geometric condition for observability in the case of the wave equation posed on a bounded domain with smooth boundary. In this talk, I shall explain how a similar condition allows observing the solution of quantum dynamical equations, with explicit constants, and under minimal regularity conditions on the driving potential. The approach used here is based on a quantum analogue of the Wasserstein distance used to measure the proximity of a quantum density operator to its classical limit.