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...

We develop rate-distortion theory for individual data with respect to general distortion measures, that is, a theory of lossy compression of individual data. This is applied to Euclidean distortion, Hamming distortion, Kolmogorov distortion, and Shannon-Fano distortion. We show that in all these cases for every function satisfying the obvious constraints there are data that have this function a...