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International Journal of Quantum Information

INFLUENCE OF ENTANGLEMENT IN QUANTUM PARRONDO GAME

KUI XU, Liusheng Huang, Wei Yang

Published Dec 1, 2008• 2 citations
Publisher

Abstract

Classical Parrondo game shows that the combination of two losing games can achieve a winning result. We investigate such an effect under quantum models, and make a complete research about the initial states that can be adapted. By the comparison of the payoffs which come from the GHZ class, W class and initial states without entanglement, we find out that entanglement plays an important role here. Moreover, we reveal that, particular initial state without entanglement can even provide us optimal payoff. Thorough discussion and exact results in this article will help us not only to make appropriate choices in quantum Parrondo game, but also have a deeper understanding about entanglement and quantum game.

DOI
10.1142/s0219749908004468

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Classical Parrondo game shows that the combination of two losing games can achieve a winning result. We investigate such an effect under quantum models, and make a complete research about the initial states that can be adapted. By the comparison of the payoffs which come from the GHZ class, W class and initial states without entanglement, we find out that entanglement plays an important role here. Moreover, we reveal that, particular initial state without entanglement can even provide us optimal payoff. Thorough discussion and exact results in this article will help us not only to make appropriate choices in quantum Parrondo game, but also have a deeper understanding about entanglement and quantum game.
It is possible to have two games that are losing when played in isolation but that, because of some form of feedback, produce a winning game when played alternately or even in a random mixture. This effect is known as Parrondo's paradox. Quantum mechanics provides novel methods of combining two games through interference and entanglement. Two models of quantum Parrondo's games have been published and these are reviewed here. We speculate on a model of a quantum Parrondo's game using entanglement. Such games could find a use in the development of algorithms for quantum computers.
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 the 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 the Parrondo sequence may generate a 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.
We analyse the role of degree of entanglement for Vaidman's game in a setting where the players share a set of partially entangled three-qubit states. Our results show that the entangled states combined with quantum strategies may not be always helpful in winning a game as opposed to the classical strategies. We further find the conditions under which quantum strategies are always helpful in achieving higher winning probability in the game in comparison to classical strategies. Moreover, we show that a special class of W states can always be used to win the game using quantum strategies irrespective of the degree of entanglement between the three qubits. Our analysis also helps us in comparing the Vaidman's game with the secret sharing protocol. Furthermore, we propose a new Vaidman-type game where the rule maker itself is entangled with the other two players and acts as a facilitator to share a secret key with the two players.
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.
The well-known counterintuitive phenomenon, where the combination of unfavorable situations can establish favorable ones, is called Parrondo's paradox. Here, 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 the different periods. Moreover, we also analyze the relationships between Parrondo's games and quantum entanglement in our scheme. Along with the applications of different kinds of quantum walks, our outcomes potentially encourage the development of new quantum algorithms.