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Territories of Parrondo’s paradox and its entanglement dynamics in quantum walks

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Abstract

Parrondo’s paradox is a well-known counterintuitive phenomenon, where the combination of unfavorable situations can establish favorable ones. In this paper, we study one-dimensional discrete-time quantum walks, manipulating two different coins (two-state) operators representing two losing games A and B, respectively, to create the Parrondo effect in the quantum domain. We exhibit that games A and B are losing games when played individually but could produce a winning expectation when played alternatively for a particular sequence of different periods for distinct choices of the relative phase. Furthermore, we investigate the regimes of the relative phase of initial state of coins where Parrondo games exist. Moreover, we also analyze the relationships between Parrondo’s game and quantum entanglement and show regimes where Parrondo sequence may generate maximal entangler state in our scheme. Along with the applications of different kinds of quantum walks, our outcomes potentially encourage the development of new quantum algorithms.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: There are no observational data related to this article. The necessary calculations and graphic discussion can be made available on request].

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Acknowledgements

M. Jan and N.A.K. acknowledge the postdoctoral fellowship supported by Zhejiang Normal University under Grants No. ZC304022918 and No. ZC304022980, respectively. G.X. acknowledges support from the NSFC under Grants No. 11835011 and No. 12174346.

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Authors and Affiliations

  1. Department of Physics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Munsif Jan, Niaz Ali Khan & Gao Xianlong

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  1. Munsif Jan
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Correspondence to Munsif Jan, Niaz Ali Khan or Gao Xianlong.

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Jan, M., Khan, N.A. & Xianlong, G. Territories of Parrondo’s paradox and its entanglement dynamics in quantum walks. Eur. Phys. J. Plus 138, 65 (2023). https://doi.org/10.1140/epjp/s13360-023-03685-z

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