Direct Measurement of a 27-Dimensional Orbital-Angular-Momentum State Vector

TL;DR

This paper demonstrates a practical method for directly measuring a high-dimensional quantum state vector with 27 dimensions in the orbital-angular-momentum basis, enabling efficient characterization of complex quantum states.

Contribution

The authors experimentally implement direct measurement of a 27-dimensional orbital-angular-momentum quantum state, extending the technique to high-dimensional systems.

Findings

Successfully measured a 27-dimensional state vector

Observed the relationship between state rotations and phase shifts

Demonstrated applicability to high-dimensional quantum information

Abstract

The measurement of a quantum state poses a unique challenge for experimentalists. Recently, the technique of "direct measurement" was proposed for characterizing a quantum state in-situ through sequential weak and strong measurements. While this method has been used for measuring polarization states, its real potential lies in the measurement of states with a large dimensionality. Here we show the practical direct measurement of a high-dimensional state vector in the discrete basis of orbital-angular momentum. Through weak measurements of orbital-angular momentum and strong measurements of angular position, we measure the complex probability amplitudes of a pure state with a dimensionality, d=27. Further, we use our method to directly observe the relationship between rotations of a state vector and the relative phase between its orbital-angular-momentum components. Our technique has important applications in high-dimensional classical and quantum information systems, and can be extended to characterize other types of large quantum states.