A tomographic measurement is a ubiquitous tool for estimating the properties of quantum states, and its application is known as quantum state tomography (QST). The process involves manipulating single photons in a sequence of projective measurements, often to construct a density matrix from which other information can be inferred, and is as laborious as it is complex. Here we unravel the steps of a QST and outline how it may be demonstrated in a fast and simple manner with intense (classical) light. We use scalar beams in a time reversal approach to simulate the outcome of a QST and exploit non-separability in classical vector beams as a means to treat the latter as a “classically entangled” state for illustrating QSTs directly. We provide a complete do-it-yourself resource for the practical implementation of this approach, complete with tutorial video, which we hope will facilitate the introduction of this core quantum tool into teaching and research laboratories alike. Our work highlights the value of using intense classical light as a means to study quantum systems and in the process provides a tutorial on the fundamentals of QSTs.

中文翻译：

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量子态层析成像中的概念和强光下的经典实现：教程

层析成像测量是一种普遍使用的估算量子态性质的工具，其应用被称为量子态层析成像（QST）。该过程涉及操纵一系列投影测量中的单个光子，通常是构建一个密度矩阵，从中可以推断出其他信息，并且它非常复杂。在这里，我们将阐明QST的步骤，并概述如何在强光（经典）下快速，简单地演示QST。我们在时间反转方法中使用标量束来模拟QST的结果，并利用经典矢量束中的不可分离性作为将后者视为直接说明QST的“经典纠缠”状态的一种手段。我们为该方法的实际实施提供了一个完整的“自己动手”资源，完整的教学视频，我们希望这将有助于将此核心量子工具引入教学和研究实验室。我们的工作强调了使用强古典光作为研究量子系统的方法的价值，并在此过程中提供了有关QST基本原理的教程。