Abstract
Quantum game theory has stimulated some interest in recent years with the advancement of quantum information theory. This interest has led to a resurgence of quantum Parrondo's games. With two losing games combining to give a winning game, this paradoxical idea is known as Parrondo's paradox. By using chaotic switching between the two losing quantum games, we show that it is possible to achieve Parrondo's paradox involving a quantum walker playing two-sided quantum coin tossing games. Furthermore, we show that the framework of chaotic switching in quantum coin tosses can be applied to encryption. This is a proposal to deploy a quantum coin toss with chaotic switching for semiclassical encryption.Received 24 February 2021Accepted 18 April 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.L022019Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasControl & applications of chaosQuantum walksTechniquesChaos & nonlinear dynamicsStatistical PhysicsNonlinear Dynamics
Highlights
Parrondo’s paradox refers to the phenomenon where two individually losing games can be combined to win through deterministic or random mixing of the games [1,2,3,4,5,6,7]
We show that chaotic switching can, improve on quantum coin tossing Parrondo’s games and provide insight into how chaotic switching for quantum coin tosses can be applied to encryption
Previous research focused mainly on fundamental concepts in quantum information that may be useful in classifying operations or states in a quantum computer based on the final observed outcome
Summary
Parrondo’s paradox refers to the phenomenon where two individually losing games can be combined to win through deterministic or random mixing of the games [1,2,3,4,5,6,7]. This places chaotic switching at an added advantage over previously studied random and sequential switchings, opening up avenues for applications to modern problems. We present one such application to encryption as an illustration of our work here. The two-sided quantum coin toss random walk [15] will be the starting point of the quantum Parrondo’s games to be investigated. A Parrondo paradoxical two-sided quantum coin toss random walk, while nontrivial, can be realized through modern standards of quantum computing [25]. We discuss the method behind developing a quantum coin toss Parrondo’s game with chaotic switching. A general two-sided quantum coin is an arbitrary superposition of two
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