  Wave-particle duality has become one of the flagships of quantum mechanics.
This counter-intuitive concept is highlighted in a delayed choice experiment,
where the experimental setup that reveals either the particle or wave nature of
a quantum system is decided after the system has entered the apparatus. Here we
consider delayed choice experiments from the perspective of device-independent
causal models and show their equivalence to a prepare-and-measure scenario.
Within this framework, we consider Wheeler's original proposal and its variant
using a quantum control and show that a simple classical causal model is
capable of reproducing the quantum mechanical predictions. Nonetheless, among
other results, we show that in a slight variant of Wheeler's
Gedankenexperiment, a photon in an interferometer can indeed generate
statistics incompatible with any non-retrocausal hidden variable model whose
dimensionality is the same as that of the quantum system it is supposed to
mimic. Our proposal tolerates arbitrary losses and inefficiencies making it
specially suited to loophole-free experimental implementations.
