QUANTUM PARRONDO'S GAMES CONSTRUCTED BY QUANTUM RANDOM WALKS

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(alpha(A), beta(A), gamma(A)) and U-B(alpha(B), beta(B), gamma(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 beta(A) = 45 degrees, gamma(A) = 0, alpha(B) = 0, beta(B) = 88 degrees, we find game 1 with U-A(S) = U-S(-51 degrees, 45 degrees, 0), U-B(S) = U-S(0, 88 degrees, -16 degrees) will win and get the most profit. If we set alpha(A) = 0, beta(A) = 45 degrees, alpha(B) = 0, beta(B) = 88 degrees and game 2 with U-A(S) = U-S(0, 45 degrees, -51 degrees), U-B(S) = U-S(0, 88 degrees, -67 degrees) 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.