Device independent certification of a quantum delayed choice experiment

Wave-particle duality has long been considered a fundamental signature of the non-classical behavior of quantum phenomena, specially in a delayed choice experiment (DCE), where the experimental setup revealing either the particle or wave nature of the system is decided after the system has entered the apparatus. However, as counter-intuitive as it might seem, usual DCEs do have a simple causal explanation. Here, we take a different route and under a natural assumption about the dimensionality of the system under test, we present an experimental proof of the non-classicality of a DCE based on the violation of a dimension witness inequality. Our conclusion is reached in a device-independent and loophole-free manner, that is, based solely on the observed data and without the need on any assumptions about the measurement apparatus.