Genuine temporal correlations can certify the quantum dimension

Abstract

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 ${}^{171}$Yb${}^{+}$ ion. Our test goes beyond the prepare-and-measure scheme of previous approaches, demonstrating the advantage of genuine temporal correlations.

arXiv comment10 pages (including appendix), 3 figures

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• Certifying dimension of quantum systems by sequential projective measurements
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• Hidden nonmacrorealism: reviving the Leggett-Garg inequality with stochastic operations