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Quantum walk on circles in phase space
We propose a variation of the quantum walk on a circle in phase space by
conjoining the Hadamard coin flip with simultaneous displacement of the
walker's location in phase space and show that this generalization is a proper
quantum walk albeit over multiple concentric circles in phase instead of just
over one circle. We motivate the conjoining of Hadamard and displacement
operations by showing that the Jaynes-Cummings model for coin+walker
approximately yields this description in the dispersive limit. The quantum walk
signature is evident in the phase distribution of the walker provided that
appropriate pulse durations are applied for each coin flip.Comment: 10 pages, 5 figure