Global Probability Asymmetry for Curve‐Optimal Entropic Bounds and Additivity Certificates for Quantum Channels

ABSTRACT We introduce global probability asymmetry (GPA), a scalar computed from sorted outcome frequencies that quantifies concentration through Lorenz‐curve cumulative‐excess gaps. Our key contribution is a novel, tight entropy–asymmetry envelope: for fixed GPA in dimension , the Shannon entropy is uniquely minimized by a one‐peak‐plus‐uniform‐tail (OPPUT) distribution. This provides a closed‐form, curve‐optimal certificate and supports finite‐sample propagation via explicit Lipschitz stability of GPA. Building on this envelope, we derive coupled preparation‐uncertainty bounds for a fixed measurement pair, including a tomography‐free, count‐level form based on the overlap matrix, with an observable mismatch penalty. The method is extended to classical side information and hybridized with standard quantum‐memory overlap bounds. Finally, applying the envelope to output spectra offers a single‐letter sufficient criterion certifying two‐use additivity of minimum output entropy (MOE) for Hastings‐type random‐unitary channels, with probabilistic certification windows from matrix concentration.