Realizing Parrondo's Paradox in Single-Qubit Quantum Walks via Local Phase-Induced Spatial Inhomogeneity

Abstract: Parrondo's paradox describes a counterintuitive phenomenon where alternating between two individually losing games results in a winning expectation. While its classical origin relies on capital-dependent bias and noise-induced asymmetry, realizing a robust quantum version of the paradox has remained challenging, especially under the constraint of single-qubit coin systems. In this work, we demonstrate that a genuine quantum Parrondo effect can emerge in discrete-time quantum walks (DTQWs) by alternating two SU(2) coin operators and introducing a localized phase shift at the origin. Through a series of numerical experiments, we show that this minimal model, without entanglement or high-dimensional coins, exhibits sustained positive drift only in the presence of spatial inhomogeneity. We analyze the role of phase angle, coin parameters, and game sequences, and identify optimal regions in which constructive interference enables paradoxical transport. Our findings validate recent theoretical claims that translational symmetry breaking is essential for overcoming interference-induced cancellation, thereby enabling directed quantum motion. This work opens new possibilities for realizing counterintuitive quantum dynamics using low-resource architectures, with potential applications in quantum control, energy harvesting, and coherence-assisted transport.