Almost One Bit Violation of Minimum-Output Rényi Entropy Additivity Simultaneously at All Orders
Published in arXiv preprint, 2026
This work proves that minimum-output Rényi-entropy additivity can fail by almost one bit simultaneously for every nonnegative Rényi order. A single maximally entangled input witnesses the gap for a finite-dimensional channel with a real Stinespring isometry, with output dimension scaling cubically in the inverse accuracy. The construction combines direct products of free groups, tensorized Haagerup estimates, finite-dimensional representations, and realification, and also yields a Haar-orthogonal model that succeeds with high probability.