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Frontiers in Optics

Genuine High-Dimensional Quantum Steering

Vatshal Srivastav, Natalia Herrera Valencia, Will McCutcheon, Sébastien Designolle, Roope Uola, Nicolas Brunner, Mehul Malik

Published Jan 1, 2021• 0 citations
Publisher

Abstract

We theoretically formalise and experimentally demonstrate a notion of genuine high- dimensional quantum nonlocal steering. We demonstrate steering with a record local dimension of 15 in a 31-dimensional space.
DOI
10.1364/ls.2021.lw5f.3

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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.
Genuine high-dimensional (HD) quantum steering was recently proposed for certifying HD entanglement in the one-sided device-independent setting, as quantified by the Schmidt number [ Phys. Rev. Lett. 126 , 200404 ( 2021 ) PRLTAO 0031-9007 10.1103/PhysRevLett.126.200404 ]. As one of the central challenges in the steering test is the tolerated noise threshold, here we develop a more robust method for certifying genuine HD steering in noisy environments. We derive genuine HD steering criteria using multiple mutually unbiased bases, surpassing the previous restriction of only two measurement settings. Although the present multisetting criteria are not tight, we theoretically show that they are more robust to noise than the tight two-setting criteria. To test the practicality of our method under realistic conditions, we report an experimental demonstration using photonic orbital angular momentum entangled states in dimensions d = 3 , 4 , 5 . Our work offers a more robust way to witness the entanglement dimension in practical one-sided device-independent quantum information processing.