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.
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BibTeX
@misc{walczak2026parrondos,
title = {{Parrondo's paradox for three discrete-time quantum walks with distinct shift operators}},
author = {Zbigniew Walczak and Jarosław H. Bauer},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06568},
eprint = {2611.06568},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06568},
}
RIS
TY - UNPB
TI - Parrondo's paradox for three discrete-time quantum walks with distinct shift operators
AU - Zbigniew Walczak
AU - Jarosław H. Bauer
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06568
UR - https://arxiv.org/abs/2611.06568
AB - 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.
ER -