2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219394We introduce two additive invariants of output quantum channels. If the value of one these invariants is less than 1 then the logarithm of the inverse of its value is a positive lower bound for the regularized minimum entropy of an output quantum channel. We give a few examples in which one of these invariants is less than 1. We also study the special cases where the above both invariants are equal to 1.14 pages, a few typo correctionsQuantum Physicstext