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 counterintuitive 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.
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