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Probing the measurement process in DTQW via recurrence

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Abstract

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 by introducing sinks in a time-multiplexed quantum walk setup using a fast-switching electro-optic modulator (EOM). Monitoring the evolution of the walker over 39 steps reveals the fundamental differences of the two cases as predicted by theory: In the restart-regime, the Polya-number will gradually approach unity. In contrast, the continue-regime yields an asymptotic value of the Polya-number of 2/π, which is reached in good approximation after only four steps and then remains almost constant.

© 2017 Optical Society of America

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