Quantum Parrondo Paradox via a Single Phase Defect Symmetry Breaking and Directed Transport

Abstract

Parrondo paradox describes the counterintuitive phenomenon in which alternating two individually losing games yields a winning outcome. Extending this effect to the quantum regime has typically required high dimensional coin spaces, entangled initial states, or engineered decoherence. Here we show that a genuine and persistent quantum Parrondo effect can be realized with minimal resources a single-qubit coin, a fixed periodic sequence of two SU (2) operators, and a single localized phase defect at the origin of a discrete-time quantum walk. By breaking translational symmetry, the phase defect acts as a scattering center that enables momentum mixing and interference-induced rectification, converting two losing games into a directed quantum ratchet. We critically reassess the winning criterion and demonstrate that the position expectation value, rather than the commonly used probability asymmetry, is the appropriate metric for validating the paradox. Harmonic analysis of the drift velocity reveals a complex, resonance type dependence with high-order Fourier components, reflecting nontrivial multi-path interference at the defect site. We further show that winning strategies are associated with cyclic restoration of coin-position entanglement, and that the ratchet effect is robust across a wide range of initial states. Our results establish that spatial inhomogeneity, rather than additional quantum resources, is the essential ingredient for a sustainable quantum Parrondo effect, offering a resource efficient blueprint for directed transport on near-term quantum platforms.