We study binary discrimination of idempotent quantum channels. When the two channels share a common full-rank invariant state, we show that a simple image inclusion condition completely determines the asymptotic behavior: when it holds, a broad family of channel divergences collapse to a closed-form, single-letter expression, regularization is unnecessary, and all error exponents (Stein/Chernoff/strong-converse) are explicitly computable with no adaptive advantage. Crucially, this yields the strong converse property for this channel family, which is an important open problem for general channels. When the inclusion fails, asymmetric exponents become infinite, implying perfect asymptotic discrimination. We apply the results to GNS-symmetric channels, showing discrimination rates for large number of self iterations converge exponentially fast to those of the corresponding idempotent peripheral projections. If the two channels do not share a common invariant state, we provide a single-letter converse bound on the regularized sandwiched Rényi cb-divergence, which suffices to establish a strong converse upper bound on the Stein exponents.

翻译：我们研究幂等量子信道的二元区分问题。当两个信道共享一个共同的全秩不变态时，我们证明一个简单的像包含条件完全决定了其渐近行为：当该条件成立时，宽泛的信道散度族坍缩为闭式单字母表达式，正则化不再必要，且所有误差指数（Stein/Chernoff/强逆）均可显式计算且无自适应优势。关键地，这为这类信道族导出了强逆性质——而这对一般信道而言是一个重要的开放问题。当包含条件不成立时，非对称指数变为无穷大，意味着完美的渐近区分性。我们将结果应用于GNS-对称信道，证明大量自迭代的区分速率指数级快速收敛至相应幂等周边投影的区分速率。若两个信道不共享共同不变态，我们给出正则化夹心Rényi cb-散度的单字母逆界，这足以建立Stein指数的强逆上界。