Quantum and random walks as universal generators of probability distributions
arXiv:1609.06711 · doi:10.1103/PhysRevA.95.062326
Abstract
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a bell-shaped one in the second case. Here I show how one can impose any desired stochastic behavior (compatible with the continuity equation for the probability function) on both systems by the appropriate choice of time- and site-dependent coins. This implies, in particular, that one can devise quantum walks that show diffusive spreading without loosing coherence, as well as random walks that exhibit the characteristic fast propagation of a quantum particle driven by a Hadamard coin.
8 pages, 2 figures; revised and enlarged version
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Cited by in corpus (9)
- Controlling quantum random walk with a step-dependent coin
- Experimental Control of the Degree of Non-Classicality via Quantum Coherence
- One-dimensional quantum walks driven by two-entangled-qubit coins
- On the equivalence between quantum and random walks on finite graphs
- Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators
- Quantum walks with spatiotemporal fractal disorder
- Directivity of quantum walk via its random walk replica
- Temporal nonclassicality in continuous-time quantum walks
- Generalized quantum teleportation of shared quantum secret with quantum walks