A new device-independent dimension witness and its experimental implementation

TL;DR

This paper introduces a new device-independent dimension witness based on the CGLMP Bell inequality for four outcomes, demonstrating its experimental violation and thus certifying a system dimension of at least four.

Contribution

It presents the first experimental violation of a third-type device-independent dimension witness beyond qutrits using the CGLMP inequality.

Findings

Experimental violation of the CGLMP inequality for four outcomes.

Certifies system dimension d ≥ 4.

First demonstration of this kind beyond qutrits.

Abstract

A dimension witness is a criterion that sets a lower bound on the dimension needed to reproduce the observed data. Three types of dimension witnesses can be found in the literature: device-dependent ones, in which the bound is obtained assuming some knowledge on the state and the measurements; device-independent prepare-and-measure ones, that can be applied to any system including classical ones; and device-independent Bell-based ones, that certify the minimal dimension of some entangled systems. Here we consider the Collins-Gisin-Linden-Massar-Popescu (CGLMP) Bell-type inequality for four outcomes. We show that a sufficiently high violation of this inequality witnesses $d \geq 4$ and present a proof-of-principle experimental observation of such a violation. This presents a first experimental violation of the third type of dimension witness beyond qutrits.