Temporal correlations in quantum mechanics are the origin of several non-classical phenomena, but they depend on the dimension of the underlying quantum system. This allows one to use such correlations for the certification of a minimal Hilbert space dimension. Here we provide a theoretical proposal and an experimental implementation of a device-independent dimension test, using temporal correlations observed on a single trapped 171Yb+ ion. Our test goes beyond the prepare-and-measure scheme of previous approaches, demonstrating the advantage of genuine temporal correlations.
@article{arxiv.1811.12259,
title = {Genuine temporal correlations can certify the quantum dimension},
author = {Cornelia Spee and Hendrik Siebeneich and Timm Florian Gloger and Peter Kaufmann and Michael Johanning and Matthias Kleinmann and Christof Wunderlich and Otfried Gühne},
journal= {arXiv preprint arXiv:1811.12259},
year = {2020}
}