Decoherence in the quantum walk on the line

Abstract

We investigate the quantum walk on the line when decoherences are introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. Both mechanisms drive the system to a classical diffusive behavior. In the case of measurements, we show that the diffusion coefficient is proportional to the variance of the initially localized quantum random walker just before the first measurement. When links between neighboring sites are randomly broken with probability $p$ per unit time, the evolution becomes decoherent after a characteristic time that scales as $1/p$. The fact that the quadratic increase of the variance is eventually lost even for very small frequencies of disrupting events, suggests that the implementation of a quantum walk on a real physical system may be severely limited by thermal noise and lattice imperfections.

Elsevier style, 18 pages. New enhanced version with more material: new title, a new section was added and the discussion was updated; references added; submitted to Physica A

References in corpus (18)

• Quantum random walks - an introductory overview
• Controlling discrete quantum walks: coins and intitial states
• Quantum random walks in optical lattices
• Experimental Implementation of the Quantum Random-Walk Algorithm
• Decoherence can be useful in quantum walks
• The quantum to classical transition for random walks
• Quantum walk on the line as an interference phenomenon
• Quantum quincunx in cavity quantum electrodynamics
• Quantum random walks with decoherent coins
• Simulation of quantum random walks using interference of classical field
• Optical Cavity Implementations of the Quantum Walk
• Quantum random walk on the line as a markovian process
• One dimensional quantum walk with unitary noise
• Quantum Interference Phenomena in the Local Polarization Dynamics of Mesoscopic Systems: An NMR Observation
• Phase-space approach to the study of decoherence in quantum walks
• Decoherence in a quantum walk on the line
• Markovian Behaviour and Constrained Maximization of the Entropy in Chaotic Quantum Systems
• Symmetry of distribution for the one-dimensional Hadamard walk

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• Quantum walks: decoherence and coin-flipping games
• Chirality asymptotic behavior and non-Markovianity in quantum walks on a line
• Extraordinary behaviors in two-dimensional decoherent alternative quantum walk
• Decoherent quantum walks driven by a generic coin operation
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• The QWalk Simulator of Quantum Walks
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• Quantum correlations of identical particles subject to classical environmental noise
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• Mixing and Decoherence in Continuous-time quantum walks on long-range interacting cycles
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• Quantum walk, entanglement and thermodynamic laws
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• Tunneling effects in a one-dimensional quantum walk
• Resonant quantum kicked rotor with two internal levels
• Decoherence on Staggered Quantum Walks
• GPGPU based simulations for one and two dimensional quantum walks
• Non-markovianity and bound states in quantum walks with a phase impurity
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• On the potential of quantum walks for modeling financial return distributions
• Revivals in One-dimensional Quantum Walks with a Time and Spin-dependent Phase Shift
• Non-Markovianity in Discrete-Time Open Quantum Random Walk on Arbitrary Graphs
• Correlation effects in a discrete quantum random walk
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• Directivity of quantum walk via its random walk replica
• Coherent transport over an explosive percolation lattice
• Exact simulation of coined quantum walks with the continuous-time model
• Limit Theorems for Decoherent Two Dimensional Quantum Walks
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• Two-particle Hadamard walk on dynamically percolated line and circle
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• On the von Neumann entropy of certain quantum walks subject to decoherence