论文标题
贝叶斯对古典阴影的分析
A Bayesian analysis of classical shadows
论文作者
论文摘要
经典阴影的方法预示了量子估计的前所未有的机会，并进行了有限的测量[H.-Y. Huang，R。Kueng和J. Preskill，Nat。物理。 16，1050（2020）]。然而，它与已建立的量子断层扫描方法的关系，尤其是基于可能性模型的方法，尚不清楚。在本文中，我们通过贝叶斯平均估计（BME）的镜头研究经典阴影。在有关数值数据的直接测试中，发现BME的平均误差明显较低，但是在特定情况下，经典阴影（例如高保真地面真相状态）在完全统一的希尔伯特（Hilbert）空间中难以准确。然后，我们引入了一个可观察到的伪类似性，该时期成功地模拟了经典阴影的维度独立性和特定于状态的最优性，但在贝叶斯框架内仅确保只能确保物理状态。我们的研究揭示了古典阴影在量子状态估计中与传统思维的重要不同，以及贝叶斯方法的实用性，用于发现和形式化统计假设。
The method of classical shadows heralds unprecedented opportunities for quantum estimation with limited measurements [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020)]. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations -- such as high-fidelity ground truth states -- which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.
