CSAIL Event Calendar: Previous Series
“Counter examples to additivity of minimum output p-Renyi entropy for p close to 0.”
Speaker: Aram Harrow , University of Bristol
Relevant URL: http://qis.mit.edu/
Abstract: The additivity conjecture in quantum information theory states that entangled inputs cannot improve the rate at which classical messages can be sent over quantum channels, or equivalently that the minimum output entropy of two copies of a channel is achieved by unentangled inputs. This conjecture can be generalized by replacing von Neumann entropy with p-Renyi entropy, since the p=1 Renyi entropy is the same as the von Neumann entropy. Recently, counterexamples to this generalized additivity conjecture have been found by Dupuis, Hayden, Leung and Winter for all p>1. In this talk, I will describe counterexamples to additivity for p=0 and for a small range of p near 0. Like the p>1 counterexamples, these are also based on a randomized construction. However, we also have an explicit channel from 4 to 3 dimensions whose minimum output Renyi entropy is non-additive for all p<0.01.