Characterization of anomalous diffusion in one-dimensional quantum walks

Abstract

Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By controlling the action of quantum coin operation on the corresponding coin degree of freedom of the walker, one can demonstrate control over the diffusion behavior. In this work, we report different forms of coin operations on quantum walks exhibiting anomalous diffusion behavior. Homogeneous and accelerated quantum walks display superdiffusive behavior, whereas uncorrelated static and dynamic disorders in the evolution induce strong and weak localization of the particle indicating subdiffusive and normal diffusive behavior. The role played by the interference effects in the spreading of the walker has remained elusive and our aim in this work is to present the interplay between quantum coherence and mean squared displacement of the walker. We employ two reliable measures of coherence for conclusively establishing the role of quantum interference as the driving force behind the anomalous diffusive behavior in the dynamics of quantum walks.

arXiv commentPublished version. 8 pages, 8 figures

References in corpus (35)

• Advances in Quantum Metrology
• Quantifying Coherence
• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• A Quantum Random Walk Search Algorithm
• Exponential algorithmic speedup by quantum walk
• From quantum cellular automata to quantum lattice gases
• Local versus non-local information in quantum information theory: formalism and phenomena
• Duality of Quantum Coherence and Path Distinguishability
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
• Aperiodic Quantum Random Walks
• Quantum Walks on a Random Environment
• Optimizing the discrete time quantum walk using a SU(2) coin
• Relationship Between Quantum Walk and Relativistic Quantum Mechanics
• Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
• Quantum Walk with a time-dependent coin
• Quantum random walk on the line as a markovian process
• Wave-particle duality: an information-based approach
• Disordered quantum walk-induced localization of a Bose-Einstein condensate
• Anderson localization in generalized discrete time quantum walks
• Universal Nonlinear Disordered Wave Packet Subdiffusion: 12 Decades
• Experimental quantum verification in the presence of temporally correlated noise
• Predicting quantum advantage by quantum walk with convolutional neural networks
• Coherence, Interference and Visibility
• Experimental investigation of superdiffusion via coherent disordered Quantum Walks
• Neutrino oscillations in discrete-time quantum walk framework
• Generalized Quantum Walk in Momentum Space
• Decoherence and Visibility Enhancement in Multi-Path Interference
• Localized quantum walks as secured quantum memory
• Dynamics and energy spectra of aperiodic discrete-time quantum walks
• Continuous-time random walk for a particle in a periodic potential
• Enhanced non-Markovian behavior in quantum walks with Markovian disorder
• Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation
• Accelerated quantum walk, two-particle entanglement generation and localization