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.

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