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.

Keywords

• quantum correlations
• experiment with trapped ion
• dimension witness
• temporal inequality
• genuine temporal correlations