Two-Copy Onset of Strict Superadditivity for Measured Relative Entropy

Abstract

For faithful finite-dimensional state pairs, globally optimized measured relative entropy is additive at any fixed copy number n >= 2 exactly when the states commute. This Letter proves the criterion through an explicit phase-optimized two-copy ascent direction, separates coherent collective access from the known fresh-copy classical-feed-forward bound, gives a faithful qubit construction, and states a thermodynamic corollary only for the Gibbs-prepared isolated unitary-drive setting.