Deterministic Minimum-Output-Entropy Nonadditivity via Haagerup’s Inequality and Near-Free Permutation Representations
Published in arXiv preprint, 2026
This work gives a deterministic finite-dimensional construction witnessing minimum-output-entropy nonadditivity. For every admissible fixed output size and accuracy, a polynomial-time algorithm produces near-free permutation representations whose restricted matrices define real orthogonal Stinespring blocks and a channel with a positive tensor-square entropy gap. The analysis combines Haagerup’s inequality with deterministic spectral approximation and also converts the entropy gap into self-tensor superadditivity of the one-shot Holevo quantity.