We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular, our goal is to discriminate between two arbitrary quantum states with a prescribed error threshold $\epsilon$ when copies of the states can be required on demand. We obtain ultimate lower bounds on the average number of copies needed to accomplish the task. We give a block-sampling strategy that allows us to achieve the lower bound for some classes of states. The bound is optimal in both the symmetric as well as the asymmetric setting in the sense that it requires the least mean number of copies out of all other procedures, including the ones that fix the number of copies ahead of time. For qubit states we derive explicit expressions for the minimum average number of copies and show that a sequential strategy based on fixed local measurements outperforms the best collective measurement on a predetermined number of copies. Whereas for general states the number of copies increases as $\log 1/\epsilon$, for pure states sequential strategies require a finite average number of samples even in the case of perfect discrimination, i.e., $\epsilon =0$.

中文翻译：

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量子顺序假设检验

通过关注量子假设测试的基本任务，我们在量子信息处理中引入了顺序分析。特别地，我们的目标是区分具有规定误差阈值的两个任意量子态$\epsilon$当可以按需提供国家副本时。我们获得完成任务所需的平均副本数的最终下限。我们提供了一种块采样策略，该策略使我们能够实现某些状态类别的下限。从在所有其他过程（包括提前确定拷贝数的过程）中需要最少平均拷贝数的意义上来说，该边界在对称和非对称设置中都是最佳的。对于qubit状态，我们导出了最小平均份数的显式表达式，并表明基于固定局部度量的顺序策略在预定份数上的效果优于最佳的集体度量。而对于一般状态，副本的数量随着$\mathrm{日志}\mathrm{1个}/\epsilon$，对于纯状态，即使在完全区分的情况下，顺序策略也需要有限的平均样本数，即 $\epsilon =0$。