A single phase defect in a single-qubit discrete-time quantum walk breaks translational symmetry to convert two losing games into persistent directed quantum ratchet transport via interference.
Di Crescenzo, ResearchGate preprint (2007), https: //www.researchgate.net/publication/2125890_A_ Parrondo_Paradox_in_Reliability_Theory
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Quantum Parrondo Paradox via a Single Phase Defect Symmetry Breaking and Directed Transport
A single phase defect in a single-qubit discrete-time quantum walk breaks translational symmetry to convert two losing games into persistent directed quantum ratchet transport via interference.