标题： 以样本最优方式使用温和测量学习量子态 显示英文标题

标题： Sample-optimal learning of quantum states using gentle measurements

摘要： 对量子态的轻柔测量不会完全坍塌初始状态。相反，它们会在初始状态的指定迹距离 $\alpha$ 处提供一个后测量态，同时伴随一个用于量子学习初始态的随机变量。 我们在此引入有限维量子系统上的 $\alpha-$局部轻柔测量（$\alpha-$LGM）类，这些测量是对乘积态的乘积测量，并通过轻柔性和量子微分隐私之间改进的关系，证明了该类别的强量子数据处理不等式（qDPI）。 我们进一步展示了轻柔量子 Neyman-Pearson 引理，表明我们的 qDPI 在小 $\alpha$情况下渐近最优。 此不等式被用来证明，对于量子层析和量子态认证，在指定精度 $\epsilon$下所需的量子态数量阶数为 $1/(\epsilon^2 \alpha^2)$。 最后，我们提出一种称为量子标签切换的 $\alpha-$LGM，它达到了这些界限。 将其转化为任意二元测量的$\alpha-$LGM 是一种通用的可实现方法。 显示英文摘要

摘要： Gentle measurements of quantum states do not entirely collapse the initial state. Instead, they provide a post-measurement state at a prescribed trace distance $\alpha$ from the initial state together with a random variable used for quantum learning of the initial state. We introduce here the class of $\alpha-$locally-gentle measurements ($\alpha-$LGM) on a finite dimensional quantum system which are product measurements on product states and prove a strong quantum Data-Processing Inequality (qDPI) on this class using an improved relation between gentleness and quantum differential privacy. We further show a gentle quantum Neyman-Pearson lemma which implies that our qDPI is asymptotically optimal (for small $\alpha$). This inequality is employed to show that the necessary number of quantum states for prescribed accuracy $\epsilon$ is of order $1/(\epsilon^2 \alpha^2)$ for both quantum tomography and quantum state certification. Finally, we propose an $\alpha-$LGM called quantum Label Switch that attains these bounds. It is a general implementable method to turn any two-outcome measurement into an $\alpha-$LGM.