Genuine High-Dimensional Quantum Steering

High-dimensional quantum entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems, offering significant advantages for quantum information processing. Certifying these stronger correlations, however, remains an important challenge, in particular in an experimental setting. Here we theoretically formalize and experimentally demonstrate a notion of genuine high-dimensional quantum steering. We show that high-dimensional entanglement, as quantified by the Schmidt number, can lead to a stronger form of steering, provably impossible to obtain via entanglement in lower dimensions. Exploiting the connection between steering and incompatibility of quantum measurements, we derive simple two-setting steering inequalities, the violation of which guarantees the presence of genuine high-dimensional steering, and hence certifies a lower bound on the Schmidt number in a one-sided device-independent setting. We report the experimental violation of these inequalities using macropixel photon-pair entanglement certifying genuine high-dimensional steering. In particular, using an entangled state in dimension d = 31, our data certifies a minimum Schmidt number of n = 15.

Automated summary

This study theoretically formalizes and experimentally demonstrates a notion of genuine high-dimensional quantum steering, showing that higher-dimensional quantum entanglement can lead to stronger steering. Simple two-setting steering inequalities are derived to certify the presence of genuine high-dimensional steering, based on the connection between steering and incompatibility of quantum measurements. The experimental violation of these inequalities using macropixel photon-pair entanglement certifies genuine high-dimensional steering, with a reported minimum Schmidt number of n = 15 for an entangled state in dimension d = 31.