Probing the measurement process in DTQW via recurrence

The measurement process plays a crucial role in quantum mechanics as it interrupts the unitary evolution of a state. The consequences are apparent when investigating the return probability (Polya-number) of a particle in a Hadamard walk on the line [1, 2]: Depending on whether the evolution is restarted or continued after the measurement, either a transient or a recurrent evolution can be observed. We investigate both cases experimentally for the first time and monitor the evolution of the walker over 39 steps, revealing the fundamental differences of the two cases as predicted by theory: In the restart-regime, the Polya-number will gradually approach 1. In contrast, the continue-regime yields an asymptotic value of 2/π.