Genuine high-dimensional quantum steering

TL;DR

This paper introduces and experimentally demonstrates a method to certify genuine high-dimensional quantum steering, providing a way to verify complex entanglement structures that surpass lower-dimensional systems, with implications for quantum information.

Contribution

The authors formalize and experimentally demonstrate a new notion of high-dimensional quantum steering, linking it to the Schmidt number and measurement incompatibility, with simple inequalities for certification.

Findings

Experimental violation of steering inequalities in 31-dimensional entanglement.

Certifies a minimum Schmidt number of 15 in high-dimensional entangled states.

Establishes a lower bound on the dimension of entanglement in a one-sided device-independent manner.

Abstract

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 formalise 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 macro-pixel 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 $n=15$.