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Parrondo's paradox is a well-known counterintuitive phenomenon, where thecombination of unfavorable situations can establish favorable ones. In thispaper, we study one-dimensional discrete-time quantum walks, manipulating twodifferent coins (two-state) operators representing two losing games A and B,respectively, to create the Parrondo effect in the quantum domain. We exhibitthat games A and B are losing games when played individually but could producea winning expectation when played alternatively for a particular sequence ofdifferent periods for distinct choices of the relative phase. Furthermore, weinvestigate the regimes of the relative phase of the initial state of coinswhere Parrondo games exist. Moreover, we also analyze the relationships betweenParrondo's game and quantum entanglement and show regimes where the Parrondosequence may generate a maximal entangler state in our scheme. Along with theapplications of different kinds of quantum walks, our outcomes potentiallyencourage the development of new quantum algorithms.

Territories of Parrondo's paradox and its relation with entanglement in quantum walks