Qunatum Parrondo's games constructed by quantum random walk

TL;DR

This paper constructs a quantum version of Parrondo's game using discrete quantum walks, demonstrating how mixing two losing quantum games can lead to winning strategies depending on parameter choices.

Contribution

It introduces a novel quantum Parrondo's game framework based on position mixing of coin operators in quantum walks, revealing conditions for winning strategies.

Findings

Certain parameter settings lead to winning outcomes.

Mixing two losing quantum games can produce winning results.

Large step numbers eventually lead to losses.

Abstract

We construct a Parrondo's game using discrete time quantum walks. Two lossing 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, \emph{et al}. If we set $\beta_{A}=45^{\circ},\gamma_{A}=0,\alpha_{B}=0,\beta_{B}=88^{\circ}$, we find the game 1\emph{}with {\normalsize $U_{A}^{S}=U^{S}(-51^{\circ},45^{\circ},0)$, $U_{B}^{S}=U^{S}(0,88^{\circ},-16^{\circ})$ will win and get the most profit.}If we set $\alpha_{A}=0,\beta_{A}=45^{\circ},\alpha_{B}=0,\beta_{B}=88^{\circ}$ and{\normalsize{} the game 2 with $U_{A}^{S}=U^{S}(0,45^{\circ},-51^{\circ})$, $U_{B}^{S}=U^{S}(0,88^{\circ},-67^{\circ})$, will win most. And}game 1\emph{}{\normalsize is equivalent to the}game\emph{}2\emph{}with the changes of sequences and steps. But at a large enough steps, the game will loss at last.