What does this equation mean?

The interesting content sits one step above that floor: what a channel that is symmetric under a conservation-relevant group action, without being the identity, is and is not entitled to conserve. Cirstoiu, Korzekwa, and Jennings addressed exactly that question for quantum channels invariant under a group G associated with a Noether charge, asking how far a G -symmetric but non-unitary channel can still deviate from conserving the associated quantity [ 1 ] . Their answer bounds that deviation, over the whole convex set of symmetric channels, by how far a given channel sits from being a closed, unitary evolution — its “unitarity” — a genuinely deeper and more general result than anything derived here. This article’s own contribution sits one step down in ambition and one step up in concreteness: not a bound over an entire family of channels, but one exact, state-dependent number for one fully named channel and one fully named pair of Hamiltonians, checkable rather than merely bounded. The adjoint identity behind $D_\Lambda$ is elementary; the discipline is in never letting that number answer a question its construction did not license, a discipline the remaining sections exist to enforce.