Experimental realization of a delayed-choice quantum walk.

Many paradoxes of quantum mechanics come from the fact that quantum systems can possess different features simultaneously, such as in wave-particle duality or quantum superposition. In recent delayed-choice experiments, a quantum system can be observed to manifest one feature such as the wave or particle nature, depending on the measurement setup, which is chosen after the system itself has already entered the measuring device; hence its behaviour is not predetermined. Here we adapt this paradigmatic scheme to multi-dimensional quantum walks. In our experiment, the way in which a photon interferes with itself in a strongly non-trivial pattern depends on its polarization, which is determined after the photon has already been detected. This is the first experiment realizing a multi-dimensional quantum walk with a single photon source and we present also the first experimental simulation of the Grover walk, a model that can be used to implement the Grover quantum search algorithm.