Entanglement of Bipartite Quantum Systems Driven by Repeated Interactions

Abstract

We consider a non-interacting bipartite quantum system H A S ⊗ H B 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 H A S and then with H B S . Even though the bipartite systems are not interacting, the interactions with the environment create an entanglement. We show that, in the limit of short interaction times, the environment creates an effective interaction Hamiltonian between the two systems. This interaction Hamiltonian is explicitly computed and we show that it keeps track of the order of the successive interactions with H A S and H B S . Particular physical models are studied, where the evolution of the entanglement can be explicitly computed. We also show the property of return of equilibrium and thermalization for a family of examples.

Classical and Quantum Parts of the Quantum Dynamics: The Discrete-Time Case

“…It has been conjecture in [3] by Attal and al. that a unitary operator that gives a random unitary CP map for all density matrices of the environment must have the form (where ϕ i is another orthonormal basis):…”

“…This is done by studying the proper operator algebra of the environment, the Environment Algebra. In order to motivate the idea behind such a definition we first recall a result of Attal, Deschamps and Pellegrini on classical environment (see [3]). …”

“…Consequently U leads to a classical action of the environment in the sense of [3], a fact which was not captured by the algebra A(U ). Remark however that U and V are linked by the relation…”

“…In this situation the equivalence between points 1. and 2. has already been proven by Attal and al. Indeed in [3] they show which unitary operators can be written in terms of classical noises emerging from the environment and characterize such noises: the obtuse random variables. This provides a discrete analogue of an essentially commutative dilation.…”

Quantum repeated interactions and the chaos game

“…It plays a key role in quantum engineering and information processing [42,43,44,45,46,47]. In relation to the repeated interaction process entropy production and entanglement have been studied in [48] and [49,50] respectively. At a given time nτ , the entropy is S n = −(1 − N n ) ln(1 − N n ) − N n ln N n .…”