Non-markovianity and bound states in quantum walks with a phase impurity
arXiv:1811.04886 · doi:10.1088/1751-8121/ab1ac5
Abstract
We study a quantum walker on a one-dimensional lattice with a single defect site characterized by a phase. The spread and localization of discrete-time quantum walks starting at the impurity site are affected by the appearance of bound states and their reflection symmetry. We quantify the localization in terms of an effective localization length averaged over all eigenstates and an effective participation ratio after time evolution averaged over all initial states. We observe that the reduced coin system dynamics undergoes oscillations in the long-time limit, the frequencies of which are related to the unitary sublattice operator and the bound state quasi-energy differences. The oscillations give rise to non-Markovian evolution, which we quantify using the trace distance and entanglement based measures of non-Markovianity. Indeed, we reveal that the degree of the non-Markovian behavior is closely related to the emergence of bound states due to the phase impurity. We also show that the considered measures give qualitatively different results depending on the number and symmetries of supported bound states. Finally, comparing localization and non-Markovianity measures, we demonstrate that the degree of non-Markovianity becomes maximum when the walker is most localized in position space.
arXiv comment10 pages, 7 figures
References in corpus (44)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
- Non-Markovian dynamics in open quantum systems
- Quantum random walks - an introductory overview
- Entanglement and non-Markovianity of quantum evolutions
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Quantum walks: a comprehensive review
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Photons Walking the Line: A quantum walk with adjustable coin operations
- Exploring Topological Phases With Quantum Walks
- Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Realization of a quantum walk with one and two trapped ions
- Universal quantum computation using the discrete time quantum walk
- Quantum walk of a trapped ion in phase space
- Decoherence and disorder in quantum walks: From ballistic spread to localization
- Decoherence in quantum walks - a review
- Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
- Non-Markovianity through accessible information
- Optimal state pairs for non-Markovian quantum dynamics
- Quantum random walks with decoherent coins
- Entanglement in coined quantum walks on regular graphs
- Decoherence in the quantum walk on the line
- Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk
- Trapping a particle of a quantum walk on the line
- Perfect state transfer and efficient quantum routing: a discrete-time quantum walk approach
- Discrete Time Quantum Walk Approach to State Transfer
- The topological classification of one-dimensional symmetric quantum walks
- Bulk-edge correspondence of one-dimensional quantum walks
- Perfect state transfer by means of discrete-time quantum walk search algorithms on highly symmetric graphs
- Decoherence in one-dimensional Quantum Walk
- Probing Measurement Induced Effects in Quantum Walks via Recurrence
- Perfect state transfer by means of discrete-time quantum walk on complete bipartite graphs
- Quantum Walks with Dynamical Control: Graph Engineering, Initial State Preparation and State Transfer
- Qubit state transfer via discrete-time quantum walks
- Complete homotopy invariants for translation invariant symmetric quantum walks on a chain
- Quantum non-Markovianity induced by Anderson localization
- Enhanced non-Markovian behavior in quantum walks with Markovian disorder
- Chirality asymptotic behavior and non-Markovianity in quantum walks on a line
- Inequivalence of Correlation-based Measures of Non-Markovianity
- Bose-Hubbard lattice as a controllable environment for open quantum systems
- From Disordered Quantum Walk to Physics of Off-diagonal Disorder
- Memory effects in a quasi-periodic Fermi lattice
- Discrete dynamics and non-Markovianity