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arXiv:1104.5275

A Quantum Analogue of Parrondo's Game

Clement Boateng Ampadu

Published Apr 28, 2011• 1 citation
arXivHTMLPDF

Abstract

We consider the discrete-time quantum walk in the plane, and present a quantum implementation of Parrondo's game for four players. Physical significance of the game strategies are also discussed.
DOI
10.48550/arxiv.1104.5275

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Parrondo's paradox is ubiquitous in games, ratchets and random walks.The apparent paradox, devised by J. M. R. Parrondo, that two losing games AAA and BBB can produce an winning outcome has been adapted in many physical and biological systems to explain their working. However, proposals on demonstrating Parrondo's paradox using quantum walks failed in the asymptotic limits. In this work, we show that instead of a single coin if we consider a two coin initial state which may or may not be entangled, we can observe a genuine Parrondo's paradox with quantum walks. Further we focus on reasons for this and pin down the asymmetry in initial two-coin state or asymmetry in shift operator, either of which are necessary for observing a genuine Parrondo's paradox. We extend our work to a 3-coin initial state too with similar results. The implications of our work for observing quantum ratchet like behavior using quantum walks is also discussed.