Rényi Entropy Additivity Fails Outside Midrange
Finite-dimensional projection-induced quantum channels violate minimum output p-Rényi entropy additivity for p>3/4 and 0≤p<1/4, leaving [1/4, 3/4] unresolved.
TL;DR — The paper proves finite-dimensional projection-induced quantum-channel counterexamples to minimum output p-Rényi entropy additivity for p>3/4 and 0≤p<1/4. It reduces the unresolved part of 0<p<1 to [1/4, 3/4] and improves a von Neumann entropy output-dimension threshold without stating the numerical threshold in the abstract.
Core result
The paper addresses additivity of minimum output entropies, which the abstract calls a central problem in quantum information theory.
Its main result is an existence theorem: for every Rényi order p with p>3/4 or 0≤p<1/4, there are finite-dimensional projection-induced quantum channels for which additivity of minimum output p-Rényi entropy fails.
The result narrows the unresolved part of the subunit interval 0<p<1 to [1/4, 3/4].
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