Measurements in two bases are sufficient for certifying high-dimensional entanglement

TL;DR

This paper demonstrates that measurements in just two bases, including a non-orthonormal one, can efficiently certify high-dimensional entanglement in quantum systems, validated through experiments with photon orbital angular momentum.

Contribution

It introduces a practical method for certifying high-dimensional entanglement using only two measurement bases, avoiding full state tomography.

Findings

Successfully certified 9-dimensional entanglement in photons.

Achieved certification in 11-dimensional subspaces per photon.

Validated the method under realistic experimental conditions.

Abstract

High-dimensional encoding of quantum information provides a promising method of transcending current limitations in quantum communication. One of the central challenges in the pursuit of such an approach is the certification of high-dimensional entanglement. In particular, it is desirable to do so without resorting to inefficient full state tomography. Here, we show how carefully constructed measurements in two bases (one of which is not orthonormal) can be used to faithfully and efficiently certify bipartite high-dimensional states and their entanglement for any physical platform. To showcase the practicality of this approach under realistic conditions, we put it to the test for photons entangled in their orbital angular momentum. In our experimental setup, we are able to verify 9-dimensional entanglement for a pair of photons on a 11-dimensional subspace each, at present the highest amount certified without any assumptions on the state.