Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators

Abstract

Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I show that this is not the only way: I introduce a quantum walk driven by an inhomogeneous, time-dependent coin operator, which mimics the statistical properties of a random walk at all time scales. The quantum particle undergoes unitary evolution and, in fact, the high correlation evidenced by the components of the wave function can be used to revert the outcome of an accidental measurement of its chirality.

4 pages, 2 figures; Revised and extended version: 8 pages, 6 figures

References in corpus (8)

• Universal computation by quantum walk
• Decoherence in quantum walks - a review
• Asymptotic evolution of quantum walks with random coin
• Observation of quasiperiodic dynamics in a one-dimensional quantum walk of single photons in space
• Non-independent continuous time random walks
• The Limiting Distribution of Decoherent Quantum Random Walks
• Invariance in quantum walks with time-dependent coin operators
• Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality

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• Quantum and random walks as universal generators of probability distributions
• Measurement induced quantum walks
• Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states
• Maximal coin-position entanglement generation in a quantum walk for the third step and beyond regardless of the initial state
• Negative correlations can play a positive role in disordered quantum walks
• Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator
• Transfiguration of Quantum Walks on a line
• Quantum walks with spatiotemporal fractal disorder
• Response to glassy disorder in coin on spread of quantum walker
• Temporal nonclassicality in continuous-time quantum walks