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Parrondo’s paradox in quantum walks with different shift operators

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Abstract

Parrondo’s paradox refers to an unexpected effect when some combination of biased quantum walks shows a counterintuitive inversion of the bias direction. To date this effect was studied in the case of one-dimensional discrete-time quantum walks with deterministic sequences of two or more quantum coins and one shift operator. In the present work, we show that Parrondo’s paradox may also occur for one coin and two different shift operators which create deterministic periodic or aperiodic sequences. Moreover, we demonstrate how Parrondo’s paradox affects the time evolution of the walker-coin quantum entanglement for this kind of quantum walks.

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Authors and Affiliations

  1. Department of Theoretical Physics, Faculty of Physics and Applied Informatics, University of Lodz, Pomorska 149/153, 90-236, Lodz, Poland

    Zbigniew Walczak & Jarosław H. Bauer

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  1. Zbigniew Walczak
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  2. Jarosław H. Bauer
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Z.W. prepared all calculations and figures. J.H.B. wrote the main manuscript text. Both authors reviewed the manuscript.

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Correspondence to Jarosław H. Bauer.

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Walczak, Z., Bauer, J.H. Parrondo’s paradox in quantum walks with different shift operators. Quantum Inf Process 23, 408 (2024). https://doi.org/10.1007/s11128-024-04614-4

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