Skip to Main content Skip to Navigation
Journal articles

Open Quantum Random Walks

Abstract : 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.
Complete list of metadata

Cited literature [6 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00581553
Contributor : Aurélie Reymond Connect in order to contact the contributor
Submitted on : Thursday, March 31, 2011 - 4:13:49 PM
Last modification on : Monday, June 28, 2021 - 2:26:03 PM
Long-term archiving on: : Saturday, December 3, 2016 - 8:58:30 PM

File

DQRW.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00581553, version 2

Citation

Stephane Attal, Francesco Petruccione, Christophe Sabot, Ilya Sinayskiy. Open Quantum Random Walks. Journal of Statistical Physics, Springer Verlag, 2012, 4, pp.832-852. ⟨hal-00581553v2⟩

Share

Metrics

Les métriques sont temporairement indisponibles