We consider the sequential quantum channel discrimination problem using
adaptive and non-adaptive strategies. In this setting the number of uses of the
underlying quantum channel is not fixed but a random variable that is either
bounded in expectation or with high probability. We show that both types of
error probabilities decrease to zero exponentially fast and, when using
adaptive strategies, the rates are characterized by the measured relative
entropy between two quantum channels, yielding a strictly larger region than
that achievable by non-adaptive strategies. Allowing for quantum memory, we see
that the optimal rates are given by the regularized channel relative entropy.
Finally, we discuss achievable rates when allowing for repeated measurements
via quantum instruments and conjecture that the achievable rate region is not
larger than that achievable with POVMs by connecting the result to the strong
converse for the quantum channel Stein’s Lemma.