Counterexamples to additivity of minimum output $p$-Rényi entropy of quantum channels for all $p\ge 0$

The additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every Rényi order $p>1$, at the von Neumann point $p=1$, and for sufficiently small positive $p$, while much of the interval $0<p<1$ has remained open. In this work, we prove tha