Sequential Quantum Channel Discrimination

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, by using adaptive strategies for the discrimination problem, both types of error probabilities decrease to zero exponentially fast and the rates are characterized by the measured relative entropy between two quantum channels. Allowing for quantum memory, we see that the optimal rates are given by the regularized channel relative entropy. We also characterize the error exponents in the discrimination problem if non-adaptive strategies are used.