Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision (abstention) is allowed to vanish any possibility of errors when a conclusive result is obtained. In both scenarios, the testing between quantum states is relatively well understood, for example, the ultimate limits of the performance are established decades ago; however, the testing between quantum channels is less understood. Although the ultimate limit of minimum error discrimination between channels has been explored recently, the corresponding limit of unambiguous discrimination is unknown. In this paper, we formulate an approximate unambiguous discrimination scenario, and derive the ultimate limits of the performance for both states and channels. In particular, in the channel case, our lower bound of the inconclusive probability holds for arbitrary adaptive sensing protocols. For the special class of “teleportation-covariant” channels, the lower bound is achievable with maximum entangled inputs and no adaptive strategy is necessary.

中文翻译：

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近似明确歧视的极限

量子假设测试是量子信息处理的重要工具。两种主要策略已被广泛采用：在最小错误识别策略中，平均错误概率最小化。而在明确的歧视策略中，当获得结论性结果时，允许作出不确定性决定（弃权）以消除任何可能的错误。在这两种情况下，量子状态之间的测试都相对容易理解，例如，性能的极限已经在几十年前确立了。但是，对量子通道之间的测试了解较少。尽管最近已经研究了信道之间最小错误鉴别的极限，但不清楚相应的鉴别极限。在本文中，我们制定了一个近似明确的歧视方案，并得出了状态和信道性能的最终极限。特别是在信道情况下，我们不确定性概率的下限适用于任意自适应感应协议。对于特殊类别的“运输协变”通道，最大的纠缠输入可以实现下界，并且不需要自适应策略。