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Transport properties in directed quantum walks on the line

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Abstract

We obtained analytical expressions considering a directed continuous-time quantum walk on a directed infinite line using Bessel functions, expanding previous results in the literature, for a general initial condition. We derive the equation for the probability distribution and show how to recover normal and enhanced decay rates for the survival probability by adjusting the phase factor of the direction of the graph. Our result shows that the mean and standard deviation for a specific non-local initial condition do not depend on the direction.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Notes

  1. https://github.com/JaimePSantos/QWAK.

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Funding

This study was financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. This work is financed by National Funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) within projects UIDB/50014/2020 and IBEX (PTDC/CCI-COM/4280/2021).

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Authors and Affiliations

  1. National University of Ireland Galway, Galway, Ireland

    Bruno Chagas

  2. Irish Centre for High-End Computing, Galway, Ireland

    Bruno Chagas

  3. Haslab, INESC TEC, Porto, Portugal

    Jaime Santos

  4. Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Rodrigo Chaves

Authors
  1. Rodrigo Chaves
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  2. Jaime Santos
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  3. Bruno Chagas
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Correspondence to Rodrigo Chaves.

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Chaves, R., Santos, J. & Chagas, B. Transport properties in directed quantum walks on the line. Quantum Inf Process 22, 144 (2023). https://doi.org/10.1007/s11128-023-03874-w

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