Speaker
Description
Recurrence means a return of the dynamical system to its initial state. Classical result of Polya [1] from 1920’s shows that a random walk on a line and a 2D grid returns to the origin with certainty, while it is transient on higher-dimensional lattices. For quantum walks, detection of recurrence requires partial measurement after each step [2], yielding a conditional quantum dynamics. Combination of measurement induced effects and faster spreading implies that a quantum walk on a line can escape to infinity without ever returning to the origin. We present a demonstration of this behaviour in a photonic time-multiplexing set-up [3], which was done in collaboration with the experimental group of Christine Silberhorn from University of Paderborn. Partial measurements were implemented by deterministic out-coupling by fast-switching EOMs, allowing to address specific time-bins of the optical signal without destroying the coherence of the remaining ones. We also discuss a recent extension of the study of recurrence to quantum stochastic walks [4], which interpolates between quantum and classical walk dynamics. Surprisingly, we find that introducing classical randomness can reduce the recurrence probability --- despite the fact that the classical random walk returns with certainty --- and we identify the conditions under which this intriguing phenomenon occurs.
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