论文标题
von Neumann测量的存储和检索
Storage and retrieval of von Neumann measurements
论文作者
论文摘要
这项工作研究了从有限数量的副本中学习尺寸$ d $的未知von Neumann测量的问题。为了获得对给定测量的忠实近似，我们可以使用$ n $ times。我们的主要目标是估计一般$ n \ rightarrow 1 $学习方案的平均保真度功能最大值的最大值$ f_d $的渐近行为。我们表明，$ f_d = 1-θ\ left（\ frac {1} {n^2} \ right）$用于任意尺寸，但固定尺寸$ d $。除此之外，我们以$ d = 2 $的方式比较了各种学习方案。我们观察到，基于确定性端口的传送的学习方案在渐近上是最佳的，但对于低$ n $的性能很差。特别是，我们发现了一种并行学习方案，尽管缺乏渐近最优性，但它为低值$ n $的忠诚度提供了很高的价值，并且仅使用了两个Qubit的纠缠内存状态。
This work examines the problem of learning an unknown von Neumann measurement of dimension $d$ from a finite number of copies. To obtain a faithful approximation of the given measurement we are allowed to use it $N$ times. Our main goal is to estimate the asymptotic behavior of the maximum value of the average fidelity function $F_d$ for a general $N \rightarrow 1$ learning scheme. We show that $F_d = 1 - Θ\left(\frac{1}{N^2}\right)$ for arbitrary but fixed dimension $d$. In addition to that, we compared various learning schemes for $d=2$. We observed that the learning scheme based on deterministic port-based teleportation is asymptotically optimal but performs poorly for low $N$. In particular, we discovered a parallel learning scheme, which despite its lack of asymptotic optimality, provides a high value of the fidelity for low values of $N$ and uses only two-qubit entangled memory states.
