Quantum Walks on a Random Environment

Abstract

Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is contrasted with the decoherence effect of dynamic disorder having strength W, where a quantum to classical crossover at time $t_c\propto W^{-2}$ transforms the quantum walk into an ordinary random walk with diffusive spreading. We demonstrate these localization and decoherence phenomena in quantum carpets of the observed time evolution and examine in detail a dimer lattice which corresponds to a single qubit subject to randomness.

7 pages 8 figures (for high resolution figures send an email to [email protected])

References in corpus (3)

• Connecting the discrete and continuous-time quantum walks
• Low-frequency noise as a source of dephasing of a qubit
• Decoherence vs entanglement in coined quantum walks

Cited by in corpus (8)

• Realization of quantum walks with negligible decoherence in waveguide lattices
• Discrete single-photon quantum walks with tunable decoherence
• Disordered quantum walk-induced localization of a Bose-Einstein condensate
• Exact analytical results for quantum walks on star graph
• Dynamics of continuous-time quantum walks in restricted geometries
• Coherent transport on Apollonian networks and continuous-time quantum walks
• Continuous deformations of the Grover walk preserving localization
• Dynamical Localization of Quantum Walks in Random Environments