  It is well known that for the discrimination of classical and quantum
channels in the finite, non-asymptotic regime, adaptive strategies can give an
advantage over non-adaptive strategies. However, Hayashi [IEEE Trans. Inf.
Theory 55(8), 3807 (2009)] showed that in the asymptotic regime, the
exponential error rate for the discrimination of classical channels is not
improved in the adaptive setting. We extend this result in several ways. First,
we establish the strong Stein's lemma for classical-quantum channels by showing
that asymptotically the exponential error rate for classical-quantum channel
discrimination is not improved by adaptive strategies. Second, we recover many
other classes of channels for which adaptive strategies do not lead to an
asymptotic advantage. Third, we give various converse bounds on the power of
adaptive protocols for general asymptotic quantum channel discrimination.
Intriguingly, it remains open whether adaptive protocols can improve the
exponential error rate for quantum channel discrimination in the asymmetric
Stein setting. Our proofs are based on the concept of amortized
distinguishability of quantum channels, which we analyse using data-processing
inequalities.
