Reliability function of general classical-quantum channel

In information theory, the reliability function and its bounds, describing the exponential behavior of the error probability, are important quantitative characteristics of the channel performance. From a more general point of view, these bounds provide certain measures of distinguishability of a given set of classical states, In the paper [3], quantum analogs of the random coding and expurgation lower bounds fur the case of pure signal states were introduced. Here we discuss the case of general quantum states, in particular, we prove the expurgation bound conjectured in [3] and find the quantum cutoff rate for arbitrary mixed signal states.