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.
Romanelli, Physical Review A 80, 042332 (2009)
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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.