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

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.

8 pages, 3 figures

References in corpus (6)

• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Efficient separation of the orbital angular momentum eigenstates of light
• Influence of Atmospheric Turbulence on Optical Communications using Orbital Angular Momentum for Encoding
• Rapid Generation of Light Beams Carrying Orbital Angular Momentum
• Fourier relationship between angular position and optical orbital angular momentum
• Near-Perfect Sorting of Orbital Angular Momentum and Angular Position States of Light

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