Martínez Vargas Esteban, Hirche Christoph, Sentís Gael, Skotiniotis Michalis, Carrizo Marta, Muñoz-Tapia Ramon, Calsamiglia John
Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellatera (Barcelona) Spain.
QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark.
Phys Rev Lett. 2021 May 7;126(18):180502. doi: 10.1103/PhysRevLett.126.180502.
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 ε 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 log1/ε, for pure states sequential strategies require a finite average number of samples even in the case of perfect discrimination, i.e., ε=0.
我们通过关注量子假设检验的基本任务，引入量子信息处理中的序贯分析。特别地，我们的目标是当可以按需获取态的副本时，以规定的误差阈值ε区分两个任意量子态。我们得到了完成该任务所需平均副本数的最终下界。我们给出了一种块采样策略，它使我们能够在某些类别的态上达到下界。从在所有其他过程（包括提前固定副本数的过程）中需要最少平均副本数的意义上来说，该界在对称和非对称设置中都是最优的。对于量子比特态，我们推导出了最小平均副本数的显式表达式，并表明基于固定局部测量的序贯策略优于对预定数量副本进行的最佳集体测量。对于一般态，副本数随log1/ε增加，而对于纯态，即使在完美区分（即ε = 0）的情况下，序贯策略也需要有限的平均样本数。
