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

• Published in: European physical journal plus Vol. 138; no. 1; p. 65
• Main Authors: Jan, Munsif, Khan, Niaz Ali, Xianlong, Gao
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 21-01-2023; Springer Nature B.V
• Subjects: Algorithms; Applied and Technical Physics; Atomic; Coins; Complex Systems; Condensed Matter Physics; Game theory; Games; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Paradoxes; Phase transitions; Physics; Physics and Astronomy; Probability; Probability distribution; Quantum entanglement; Regular Article; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-023-03685-z

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.