Quantum Sequential Hypothesis Testing

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