Inhibition of spreading in quantum random walks due to quenched Poisson-distributed disorder
arXiv:1806.04024 · doi:10.1103/PhysRevA.99.042329
Abstract
We consider a quantum particle (walker) on a line who coherently chooses to jump to the left or right depending on the result of toss of a quantum coin. The lengths of the jumps are considered to be independent and identically distributed quenched Poisson random variables. We find that the spread of the walker is significantly inhibited, whereby it resides in the near-origin region, with respect to the case when there is no disorder. The scaling exponent of the quenched-averaged dispersion of the walker is sub-ballistic but super-diffusive. We also show that the features are universal to a class of sub- and super-Poissonian distributed quenched randomized jumps.
arXiv comment7 pages, 3 figures; v2: further distributions considered, close to published version
References in corpus (32)
- Quantum Cryptography
- Classification of topological insulators and superconductors in three spatial dimensions
- 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 Walk in Position Space with Single Optically Trapped Atoms
- Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
- Exploring Topological Phases With Quantum Walks
- From quantum cellular automata to quantum lattice gases
- Realization of a quantum walk with one and two trapped ions
- Fractional quantum Hall states of atoms in optical Lattices
- Anderson localization of entangled photons in an integrated quantum walk
- Quantum walk of a trapped ion in phase space
- An example of the difference between quantum and classical random walks
- Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory
- Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
- Experimental Implementation of the Quantum Random-Walk Algorithm
- Weak limits for quantum random walks
- Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
- Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators
- Two-photon quantum walks in an elliptical direct-write waveguide array
- Quantum Walks on a Random Environment
- Localization and its consequences for quantum walk algorithms and quantum communication
- On the absence of homogeneous scalar unitary cellular automata
- Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk
- Disordered Quantum Walks in one lattice dimension
- One- and two-dimensional quantum walks in arrays of optical traps
- Disordered quantum walk-induced localization of a Bose-Einstein condensate
- Effective magnetic fields for stationary light
- Localisation, delocalisation, and topological transitions in disordered 2D quantum walks
- Quantum Walk with Jumps
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- Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator
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- Phase vs coin vs position disorder as a probe for the resilience and revival of single particle entanglement in cyclic quantum walks
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