Device-independent test of a delayed choice experiment

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