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We consider the general physical situation of a quantum system H0 interacting with a chain of exterior systems ⊗IN∗H, one after the other, during a small interval of time h and following some Hamiltonian H on H0 ⊗H. We discuss the passage to the limit to continuous interactions (h → 0) in a setup which allows to compute the limit of this Hamiltonian… (More)

- Stéphane Attal, Alain Joye
- 2006

We compute the quantum Langevin equation (or quantum stochastic differential equation) representing the action of a quantum heat bath at thermal equilibrium on a simple quantum system. These equations are obtained by taking the continuous limit of the Hamiltonian description for repeated quantum interactions with a sequence of photons at a given density… (More)

- Stéphane Attal, Alain Joye
- 2005

We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ , the reference system is coupled to one new element of the chain only, by means of an interaction of strength λ. We… (More)

A new model of quantum random walks is introduced, on lattices as well as on finite 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… (More)

- Stéphane Attal
- 2005

Open Quantum Random Walks, as developed in [1], are the exact quantum generalization of Markov chains on finite graphs or on nets. These random walks are typically quantum in their behavior, step by step, but they seem to show up a rather classical asymptotic behavior, as opposed to the quantum random walks usually considered in Quantum Information Theory… (More)

- Stéphane Attal
- 2010

This article presents several results establishing connections between Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one component that we get from a dynamical system on a product system, when losing information on the other component. We show… (More)

We consider series of iterated non-commutative stochastic integrals of scalar operators on the boson Fock space. We give a sufficient condition for these series to converge and to define a reasonable operator. An application of this criterion gives a condition for the convergence of some formal series of generalized integrator processes such as considered… (More)

Among the discrete evolution equations describing a quantum system HS undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in RN . The characterization we obtain is entirely algebraical in terms of the unitary operator driving the elementary interaction.… (More)

We consider a non-interacting bipartite quantum system HA S ⊗ HB S undergoing repeated quantum interactions with an environment modeled by a chain of independant quantum systems interacting one after the other with the bipartite system. The interactions are made so that the pieces of environment interact first with HA S and then with HB S . Even though the… (More)