Proved approximate majorization for quantum depolarizing channels, yielding tight third-order classical capacity expansion. Entangled codewords provide only O(log log n) bit advantage over product coding strategies in finite-blocklength regime.

Proved approximate majorization for quantum depolarizing channels, yielding tight third-order classical capacity expansion. Entangled codewords provide only O(log log n) bit advantage over product coding strategies in finite-blocklength regime.