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.
翻译：我们使用适应性和非适应性战略来考虑相继量子信道歧视问题。 在设定的这一设置中,基础量子信道的用途数量不是固定的,而是随机变量,该变量要么受预期的约束,要么具有很高的概率。我们发现,两种类型的误差概率都以两个量子信道之间测量的相对倍增速速度下降为零,在使用适应性战略时,该比率的特点是两个量子信道之间测量的相对倍增率,产生的区域绝对大于非适应性战略所能达到的区域。允许量子内存,我们看到,最佳速率是由正规化信道相对的倍增率给出的。最后,我们在允许通过量子仪器和假设反复测量时,通过将结果与量子通道Lemma的强反差联系起来,我们讨论了可实现的速率,即可实现率区域不会大于与POVMs的可实现率区域。
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