Detecting high-dimensional entanglement by randomized product projections

TL;DR

This paper presents a practical, resource-efficient method for detecting high-dimensional entanglement in quantum systems using randomized product projections, reducing experimental complexity and enabling reliable certification.

Contribution

It introduces a novel detection strategy based on randomized projections that simplifies entanglement certification and provides algorithms for estimating the Schmidt number with limited data.

Findings

Efficient entanglement detection using randomized product projections.

Single basis state measurement suffices for entanglement certification.

Algorithm for lower bounding Schmidt number with high confidence.

Abstract

The characterization of high-dimensional entanglement plays a crucial role in the field of quantum information science. Conventional entanglement criteria measuring coherent superpositions of multiple basis states face experimental bottlenecks on most physical platforms due to limited multi-channel control. Here, we introduce a practically efficient detection strategy based on randomized product projections. We show that the first-order moments of such projections can be used to estimate entanglement fidelity, thereby enabling practical and efficient certification of the Schmidt number in high-dimensional bipartite systems. By constructing optimal observables, it is sufficient to merely measure a single basis state, substantially reducing experimental overhead. Moreover, we present an algorithm to obtain a lower bound of the Schmidt number with a high confidence level from a limited number of experimental data. Our results open up resource-efficient experimental avenues to detect high-dimensional entanglement and test its implementations in modern information technologies.