Counterexamples to additivity of minimum output p-R'enyi entropy of quantum channels for all p 0
This work provides explicit, constructive counterexamples showing that for Rényi orders p greater than 3/4 and less than 1/4, the minimum output p-Rényi entropy of a combined quantum channel is strictly less than the sum of the individual minimum entropies. It resolves an open problem regarding the additivity of these entropies.