hal-00581553, version 1

Open Quantum Random Walks

Stephane Attal ¹, Francesco Petruccione ², Christophe Sabot ¹, Ilya Sinayskiy ²

(2011-03-30)

• 1 :  Institut Camille Jordan (ICJ)
• 
  CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon Bât. Jean Braconnier n° 101 43 Bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX France
• 2 :  Centre for Quantum Technology
• http://quantum.ukzn.ac.za/
  University of Kwazulu-Natal Quantum Research Group School of Physics and National Institute for Theoretical Physics University of KwaZulu-Natal Durban 4001, South Africa Afrique Du Sud

Versions disponibles :  v1 (31-03-2011) v2 (31-03-2011)

Références bibliographiques

• Type de publication : Documents sans référence de publication (Preprint)
• Domaine :

  Mathématiques/Physique mathématique

  Mathématiques/Probabilités

  Physique/Physique mathématique

  Physique/Physique Quantique

• Titre : Open Quantum Random Walks
• Résumé : A new model of quantum random walks is introduced, on lattices as well as on nite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogue of classical Markov chains. We explore the \quantum trajectory" point of view on these quantum random walks, that is, we show that measuring the position of the particle after each time-step gives rise to a classical Markov chain, on the lattice times the state space of the particle. This quantum trajectory is a simulation of the master equation of the quantum random walk. The physical pertinence of such quantum random walks and the way they can be concretely realized is discussed. Connections and di erences with the already well-known quantum random walks, such as the Hadamard random walk, are established. We explore several examples and compute their limit behavior. We show that the typical behavior of Open Quantum Random Walks seems to be very di erent from Hadamard-type quantum random walks. Indeed, while being very quantum in their behavior, Open Quantum Random Walks tend to become more and more classical as time goes.
• Langue du texte
  intégral : Anglais
• Date de production,
  écriture : 30/03/2011

Liste des fichiers attachés à ce document :

• hal-00581553, version 1
• http://hal.archives-ouvertes.fr/hal-00581553
• oai:hal.archives-ouvertes.fr:hal-00581553
• Contributeur : Aurélie Reymond <>
• Soumis le : Jeudi 31 Mars 2011, 09:52:20
• Dernière modification le : Jeudi 31 Mars 2011, 16:11:28