Amortized channel divergence for asymptotic quantum channel discrimination
Amortized channel divergence for asymptotic quantum channel discrimination
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DOI：
10.1007/s11005-020-01297-7
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发表时间：
2018-08
影响因子：
1.2
通讯作者：
M. Wilde;M. Berta;C. Hirche;Eneet Kaur
中科院分区：
文献类型：
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作者：
M. Wilde;M. Berta;C. Hirche;Eneet Kaur
众所周知，对于有限非渐近区域中的经典和量子信道的区分，自适应策略可以比非自适应策略提供优势。然而，Hayashi（IEEE Trans Inf Theory 55（8）：3807-3820，2009. arXiv：0804.0686）表明，在渐近状态下，在自适应设置中，用于区分经典信道的指数错误率没有改善。我们以几种方式扩展这个结果。首先，我们建立了强斯坦因引理的经典量子信道的渐近指数错误率的经典量子信道歧视不改善自适应策略。其次，我们恢复许多其他类别的自适应策略不导致渐近优势的渠道。第三，我们给出了一般渐近量子信道鉴别的自适应协议的功率的各种匡威界。有趣的是，自适应协议是否可以改善非对称Stein设置中量子信道鉴别的指数错误率仍然是开放的。我们的证明是基于量子信道的摊销可扩展性的概念，我们使用数据处理不等式进行分析。
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):3807–3820, 2009. arXiv:0804.0686) 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.