QUANTUM PARRONDQ'S GAMES CONSTRUCTED BY QUANTUM RANDOM WALKS

摘要

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 U_A(α_A, β_A, γ_A) and U_B(α_B, β_B, γ_B), 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 β_A = 45°, γ_A = 0, α_B = 0,β_B = 88°, we find game 1 with U_A~S = U~S(-51°,45°,0), U_B~S = U~S(0,88°, -16°) will win and get the most profit. If we set α_A = 0,β_A = 45°, α_B = 0,β_B = 88° and game 2 with U_A~S = U~S(0,45°, -51°),U_B~S = U~S(0,88°, -67°) 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.