Aperiodic space-inhomogeneous quantum walks: localization properties, energy spectra and enhancement of entanglement

Abstract

We study the localization properties, energy spectra and coin-position entanglement of the aperiodic discrete-time quantum walks. The aperiodicity is described by spatially dependent quantum coins distributed on the lattice, whose distribution is neither periodic (Bloch-like) nor random (Anderson-like). Within transport properties we identified delocalized/localized quantum walks mediated by a proper adjusting of aperiodic parameter. Both scenarios are studied by exploring typical quantities (inverse participation ratio and survival probability), as well as the energy spectra of an associated effective Hamiltonian. By using the energy spectra analysis, we show that the early stage the inhomogeneity leads to vanishing gap between two main bands, which justifies the the delocalized character observed for $\nu <0.5$. With increase of $\nu$ arises gaps and flat-bands on the energy spectra, which corroborates the suppresion of transport detected for $\nu >0.5$. For $\nu$ high enough we observe an energy spectra which resembles that described by the 1d Anderson model. Within coin-position entanglement, we show many settings in which an enhancement in the ability to entangle is observed. This behavior brings new informations about the role played by aperiodicity on the coin-poisition entanglement for static inhomogeneous systems, reported before as almost always reducing the entanglement when comparing with the homogeneous case. We extend the analysis in order to show that systems with static inhomogeneity are able to exhibit asymptotic limit of entanglement.

10 pages, 11 figures

References in corpus (44)

• Quantum Computation and Decision Trees
• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• A Quantum Random Walk Search Algorithm
• Universal computation by quantum walk
• Quantum walks of correlated particles
• Quantum walks: a comprehensive review
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
• Universal quantum computation using the discrete time quantum walk
• Anderson localization of entangled photons in an integrated quantum walk
• Strongly Correlated Quantum Walks in Optical Lattices
• Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
• Decoherence and disorder in quantum walks: From ballistic spread to localization
• Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
• Mott--Hubbard transition vs. Anderson localization of correlated, disordered electrons
• Experimental observation of the mobility edge in a waveguide with correlated disorder
• Connecting the discrete and continuous-time quantum walks
• Entanglement in coined quantum walks on regular graphs
• Aperiodic Quantum Random Walks
• Quantum walk on the line: entanglement and non-local initial conditions
• Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
• Trapping a particle of a quantum walk on the line
• Quantum Walk with a time-dependent coin
• One dimensional quantum walk with unitary noise
• Anderson localization in generalized discrete time quantum walks
• Chiral Quantum Walks
• Entangling Power of Disordered Quantum Walks
• Simulating Anderson localization via a quantum walk on a one-dimensional lattice of superconducting qubits
• Driving quantum walk spreading with the coin operator
• Generalized Quantum Walk in Momentum Space
• Controlling quantum random walk with a step-dependent coin
• The Elephant Quantum Walk
• Localized State in a Two-Dimensional Quantum Walk on a Disordered Lattice
• Dynamics and energy spectra of aperiodic discrete-time quantum walks
• The Fibonacci quantum walk and its cassical trace map
• Asymptotic entanglement in quantum walks from delocalized initial states
• Quantum walk of a Bose-Einstein condensate in the Brillouin zone
• Finding paths in tree graphs with a quantum walk
• Quantum Walk with Jumps
• Unusual scaling in a discrete quantum walk with random long range steps
• Skyrmion Burst and Multiple Quantum Walk in Thin Ferromagnetic Films
• Quantum entanglement and drifting generated by an AC field resonant with frequency-doubled Bloch oscillations of correlated particles
• Unidirectional quantum walk of two correlated particles: Separating bound-pair and unbound wavepacket components
• Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality

Cited by in corpus (16)

• Quantum walks with sequential aperiodic jumps
• Self-trapped quantum walks
• Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps
• Bloch-like super-oscillations and unidirectional motion of phase driven quantum walkers
• 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
• Optimizing the spatial spread of a quantum walk
• Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics
• Discrete-time quantum walk dispersion control through long-range correlations
• Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator
• Localization in Quantum Walks with a Single Lattice Defect: A Comparative Study
• Nonlinear three-state quantum walks
• Universal dynamical scaling laws in three-state quantum walks
• Quantum walks with spatiotemporal fractal disorder
• Response to glassy disorder in coin on spread of quantum walker