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):3807–3820,
2009. arXiv:0804.0686) 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.