QUANTUM PARRONDO'S GAMES CONSTRUCTED BY QUANTUM RANDOM WALKS

Abstract

We construct a Parrondo's game using discrete-time quantum walks (DTQWs). Two losing games are represented by two different coin operators. By mixing the two coin operators UA(αA, βA, γA) and UB(αB, βB, γB), we may win the game. Here, we mix the two games in position instead of time. With a number of selections of the parameters, we can win the game with sequences ABB, ABBB, etc. If we set βA = 45°, γA = 0, αB = 0, βB = 88°, we find game 1 with [Formula: see text], [Formula: see text] will win and get the most profit. If we set αA = 0, βA = 45°, αB = 0, βB = 88° and game 2 with [Formula: see text], [Formula: see text] will win most. Game 1 is equivalent to game 2 with changes in sequences and steps. But at large enough steps, the game will lose at last. Parrondo's paradox does not exist in classical situation with our model.