Concepts in quantum state tomography and classical implementation with intense light: a tutorial

TLDR

Quantum state tomography (QST) is a widely used technique that estimates quantum state properties by performing sequential projective measurements on single photons to reconstruct a density matrix, though it is laborious and complex. The study aims to demystify QST steps and provide a fast, simple demonstration using intense classical light, offering a do‑it‑yourself resource and tutorial video to promote its use in teaching and research. The authors simulate QST outcomes with scalar beams in a time‑reversal scheme and use non‑separability in classical vector beams—treated as classically entangled—to directly illustrate QST, supplying a DIY implementation and tutorial video. The work shows that intense classical light can effectively model quantum systems, providing a practical tutorial on the fundamentals of QST.

Abstract

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.