Strong Data Processing Inequalities via Sums of Squares

A hierarchy of semidefinite programming relaxations is described which gives certified upper bounds on the strong data processing (SDPI) constant of a discrete channel. The relaxations rely on a combination of tools from approximation theory and sum-of-squares techniques. By leveraging the properties of rational Padé approximants, we prove that the hierarchy converges to the true SDPI constant. Numerical experiments are performed which verify that these relaxations are very accurate even at low levels of the hierarchy.