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 (2009)] 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.

中文翻译：

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渐近量子信道鉴别的摊销信道散度

众所周知，对于有限非渐近系统中经典和量子通道的区分，自适应策略可以比非自适应策略更具优势。然而，Hayashi [IEEE Trans。信息 Theory 55(8), 3807 (2009)] 表明，在渐近状态下，在自适应设置中，经典信道判别的指数错误率没有提高。我们以多种方式扩展了这个结果。首先，我们通过证明自适应策略不会逐渐改善经典量子信道鉴别的指数错误率，从而为经典量子信道建立强斯坦因引理。其次，我们恢复了许多其他类别的通道，这些通道的自适应策略不会导致渐近优势。第三，我们给出了用于一般渐近量子信道鉴别的自适应协议的能力的各种逆界。有趣的是，自适应协议是否可以提高非对称 Stein 设置中量子信道鉴别的指数错误率仍然是开放的。我们的证明基于量子通道的摊销可区分性的概念，我们使用数据处理不等式进行分析。