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Title: Decoherence in two-dimensional quantum walks

Abstract

We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk.

Authors:
; ;  [1]
  1. Laboratorio Nacional de Computaca(tilde sign)o Cientifica, LNCC, Caixa Postal 95113, Petropolis, Rio de Janeiro 25651-075 (Brazil)
Publication Date:
OSTI Identifier:
20852882
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 74; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.74.012312; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; LATTICE FIELD THEORY; NOISE; PROBABILITY; QUANTUM DECOHERENCE; QUANTUM MECHANICS; RANDOMNESS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Oliveira, A C, Portugal, R, Donangelo, R, and Universidade Federal do Rio de Janeiro, UFRJ, Caixa Postal 68528, Rio de Janeiro, Rio de Janeiro 21941-972. Decoherence in two-dimensional quantum walks. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.74.012312.
Oliveira, A C, Portugal, R, Donangelo, R, & Universidade Federal do Rio de Janeiro, UFRJ, Caixa Postal 68528, Rio de Janeiro, Rio de Janeiro 21941-972. Decoherence in two-dimensional quantum walks. United States. https://doi.org/10.1103/PHYSREVA.74.012312
Oliveira, A C, Portugal, R, Donangelo, R, and Universidade Federal do Rio de Janeiro, UFRJ, Caixa Postal 68528, Rio de Janeiro, Rio de Janeiro 21941-972. 2006. "Decoherence in two-dimensional quantum walks". United States. https://doi.org/10.1103/PHYSREVA.74.012312.
@article{osti_20852882,
title = {Decoherence in two-dimensional quantum walks},
author = {Oliveira, A C and Portugal, R and Donangelo, R and Universidade Federal do Rio de Janeiro, UFRJ, Caixa Postal 68528, Rio de Janeiro, Rio de Janeiro 21941-972},
abstractNote = {We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk.},
doi = {10.1103/PHYSREVA.74.012312},
url = {https://www.osti.gov/biblio/20852882}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 74,
place = {United States},
year = {Sat Jul 15 00:00:00 EDT 2006},
month = {Sat Jul 15 00:00:00 EDT 2006}
}