Channel discord and distortion

Discord, originally notable as a signature of bipartite quantum correlation, in fact can be nonzero classically, i.e. arising from noisy measurements by one the two parties. Here we redefine classical discord to quantify channel distortion, contrast previous restriction state, and then show monotonic relationship between (channel) distortion. We that is equivalent (doubly stochastic) distortion numerically discovering relation total-variation distance for protocol with party having noiseless other channel. Our numerical method includes randomly generating doubly stochastic matrices channels averaging over uniform measure input messages. Connecting establishes classical, not quantum,