Entanglement dynamics and relaxation in a few-qubit system interacting with random collisions

The dynamics of a single qubit interacting by a sequence of pairwise collisions withan environment consisting of just two more qubits is analyzed. Each collision is modeled interms of a random unitary operator with a uniform probability distribution described by theuniform Haar measure. We show that the purity of the system qubit as well as the bipartiteand the tripartite entanglement reach time-averaged equilibrium values characterized by largeinstantaneous fluctuations. These equilibrium values are independent of the order of collisionamong the qubits. The relaxation to equilibrium is analyzed also in terms of an ensemble averageof random collision histories. Such average allows for a quantitative evaluation and interpretationof the decay constants. Furthermore a dependence of the transient dynamics on the initial degree ofentanglement between the environment qubits is shown to exist. Finally the statistical propertiesof bipartite and tripartite entanglement are analyzed.