A dimensionality and purity measure for high-dimensional entangled states

TL;DR

This paper introduces a simple, direct method to measure the dimensionality and purity of high-dimensional entangled quantum states using projective measurements, applicable to photonic systems with orbital angular momentum.

Contribution

The authors present a novel approach that simultaneously quantifies entanglement dimensionality and purity through a scalable, projective measurement technique, improving state characterization efficiency.

Findings

Successfully measured high-dimensional entanglement over various purities.

Demonstrated the method with photons carrying orbital angular momentum.

Validated the approach's accuracy and simplicity for mixed states.

Abstract

High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with entanglement dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using transverse spatial modes of photons that carry orbital angular momentum and verify high-dimensional entanglement over a wide range of state purities. Our approach advances the high-dimensional tool box for characterising quantum states by providing a simple and direct dimensionality and purity measure, even for mixed entangled states.