Unmonitored and monitored recurrence in single-photon quantum walks

Recurrence is an interesting property that describes whether the walker will eventually return to the origin on infinite lattices in classical random walks. Since measurement collapse affects the wave function of the walker, in the quantum case, there are two schemes for studying recurrence properties in quantum walks (QWs) depending on how the measurement process is described. One involves restarting after measurements, known as unmonitored measurements, while the other entails monitoring after each step, referred to as monitored measurements. In this paper, we utilize the dependence of recurrence probabilities on the coin parameter to construct biased-coin QWs on a line and investigate the recurrence properties of both schemes. Based on the bulk-optics framework and using a single-photon source, we experimentally demonstrate the distinct recurrence behaviors resulting from the different evolution processes of the walker in the two schemes. This work showcases diverse recurrence properties in single-particle QW systems, thereby enhancing our understanding of measurement-induced recurrence.