Direct measurement of a one-million-dimensional photonic state

TL;DR

This paper introduces a novel method for directly measuring a million-dimensional photonic quantum state in a single measurement, significantly advancing high-dimensional quantum system characterization and classical complex field measurement.

Contribution

The authors develop a technique combining weak and strong measurements to directly access a high-dimensional quantum state, enabling real-time characterization of systems previously too complex to measure efficiently.

Findings

Measured a photonic state with approximately one million dimensions

Achieved a measurement dimension four orders of magnitude larger than previous methods

Demonstrated high-speed, high-resolution complex field measurement for classical applications

Abstract

Retrieving the vast amount of information carried by a photon is an enduring challenge in quantum metrology science and quantum photonics research. The transverse spatial state of a photon is a convenient high-dimensional quantum system for study, as it has a well-understood classical analogue as the transverse complex field profile of an optical beam. One severe drawback of all currently available quantum metrology techniques is the need for a time-consuming characterization process, which scales very unfavorably with the dimensionality of the quantum system. Here we demonstrate a technique that directly measures a million-dimensional photonic spatial state in a single setting. Through the arrangement of a weak measurement of momentum and parallel strong measurements of position, the complex values of the entire photon state vector become measurable directly. The dimension of our measured state is approximately four orders of magnitude larger than previously measured. Our work opens up a practical route for characterizing high-dimensional quantum systems in real time. Furthermore, our demonstration also serve as a high-speed, extremely-high-resolution unambiguous complex field measurement technique for diverse classical applications.