Relaxation due to random collisions with a many-qudit environment

We analyze the dynamics of a system qudit of dimension \mu sequentially interacting with the \nu-dimensional qudits of a chain playing the role of an environment. Each pairwise collision has been modeled as a random unitary transformation. The relaxation to equilibrium of the purity of the system qudit, averaged over random collisions, is analytically computed by means of a Markov chain approach. In particular, we show that the steady state is the one corresponding to the steady state for random collisions with a single environment qudit of effective dimension \nu e=\nu\mu. Finally, we numerically investigate aspects of the entanglement dynamics for qubits (\mu =\nu=2) and show that random unitary collisions can create multipartite entanglement between the system qudit and the qudits of the chain.