Optimized detection of high-dimensional entanglement

TL;DR

This paper presents a flexible, automated method for constructing optimal entanglement detection tests applicable to high-dimensional quantum states, including unfaithful states, and demonstrates its experimental implementation in photonic systems.

Contribution

The authors introduce a novel automated approach to design optimal entanglement detection protocols for arbitrary high-dimensional states, surpassing traditional fidelity-based methods.

Findings

Successfully certified 2- and 3-unfaithful entanglement in 4D photonic states

Implemented protocols using only 3 measurement settings

Detected entanglement with over 50% noise in experimental states

Abstract

Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect entanglement within a large class of entangled quantum states, the so-called unfaithful states. In this paper, we introduce a highly flexible automated method to construct optimal tests for entanglement detection given a bipartite target state of arbitrary dimension, faithful or unfaithful, and a set of local measurement operators. By restricting the number or complexity of the considered measurement settings, our method outputs the most convenient protocol which can be implemented using a wide range of experimental techniques such as photons, superconducting qudits, cold atoms or trapped ions. With an experimental quantum optics setup that can prepare and measure arbitrary high-dimensional mixed states, we implement some $3$-setting protocols generated by our method. These protocols allow us to experimentally certify 2- and 3-unfaithful entanglement in 4-dimensional photonic states, some of which contain well above 50% of noise.