On hypercontractivity and a data processing inequality
Venkat Anantharam, Amin Gohari, Sudeep Kamath, Chandra Nair · 2014
In this paper we provide the correct tight constant to a data-processing inequality claimed by Erkip and Cover. The correct constant turns out to be a particular hypercontractivity parameter of (X,Y), rather than their squared maximal correlation. We also provide alternate geometric characterizations for both maximal correlation as well as the hypercontractivity parameter that characterizes the data-processing inequality.