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Title: Quantum walks with random phase shifts

Abstract

We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail the role of decoherence in quantum walks and to investigate the quantum-to-classical transition. We also provide classical analog of the quantum random walks studied. Interestingly enough, it turns out that the classical counterparts of some quantum random walks are classical random walks with a memory and biased coin. In addition random phase shifts 'simplify' the dynamics (the cross-interference terms of different paths vanish on average) and enable us to give a compact formula for the dispersion of such walks.

Authors:
 [1];  [1];  [2]
  1. Research Center for Quantum Information, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia)
  2. Department of Physics, Hunter College of CUNY, 695 Park Avenue, New York, New York 10021 (United States)
Publication Date:
OSTI Identifier:
20853027
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 74; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.74.022310; (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; AMPLITUDES; INTERFERENCE; PHASE SHIFT; QUANTUM DECOHERENCE; QUANTUM MECHANICS; RANDOMNESS

Citation Formats

Kosik, Jozef, Quniverse, Liscie udolie 116, 841 04 Bratislava, Buzek, Vladimir, Abteilung fuer Quantenphysik, Universitaet Ulm, 89069 Ulm, and Hillery, Mark. Quantum walks with random phase shifts. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.74.022310.
Kosik, Jozef, Quniverse, Liscie udolie 116, 841 04 Bratislava, Buzek, Vladimir, Abteilung fuer Quantenphysik, Universitaet Ulm, 89069 Ulm, & Hillery, Mark. Quantum walks with random phase shifts. United States. https://doi.org/10.1103/PHYSREVA.74.022310
Kosik, Jozef, Quniverse, Liscie udolie 116, 841 04 Bratislava, Buzek, Vladimir, Abteilung fuer Quantenphysik, Universitaet Ulm, 89069 Ulm, and Hillery, Mark. 2006. "Quantum walks with random phase shifts". United States. https://doi.org/10.1103/PHYSREVA.74.022310.
@article{osti_20853027,
title = {Quantum walks with random phase shifts},
author = {Kosik, Jozef and Quniverse, Liscie udolie 116, 841 04 Bratislava and Buzek, Vladimir and Abteilung fuer Quantenphysik, Universitaet Ulm, 89069 Ulm and Hillery, Mark},
abstractNote = {We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail the role of decoherence in quantum walks and to investigate the quantum-to-classical transition. We also provide classical analog of the quantum random walks studied. Interestingly enough, it turns out that the classical counterparts of some quantum random walks are classical random walks with a memory and biased coin. In addition random phase shifts 'simplify' the dynamics (the cross-interference terms of different paths vanish on average) and enable us to give a compact formula for the dispersion of such walks.},
doi = {10.1103/PHYSREVA.74.022310},
url = {https://www.osti.gov/biblio/20853027}, journal = {Physical Review. A},
issn = {1050-2947},
number = 2,
volume = 74,
place = {United States},
year = {Tue Aug 15 00:00:00 EDT 2006},
month = {Tue Aug 15 00:00:00 EDT 2006}
}