Parrondo's paradox for three discrete-time quantum walks with distinct shift operators

Abstract:Parrondo's paradox describes a surprising phenomenon in which certain combinations of biased quantum walks result in an unexpected reversal of their bias direction. To date, research on this effect has predominantly focused on one-dimensional discrete-time quantum walks that employ fixed sequences of two or three quantum coins, paired with a single shift operator. In this work, we first introduce a wide class of unitary shift operators which allow for three movement options (left, right or stay in place) of a walker in one time step, and we then demonstrate that Parrondo's paradox can also arise with a single coin and three distinct shift operators. Furthermore, we investigate how this paradox influences the time evolution of quantum entanglement between the walker and the coin in such quantum walks.

arXiv:2611.06568 [quant-ph]

(or arXiv:2611.06568v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.06568 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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