Qubit thermalization by random pulses: Asymptotic state factorization

Here we consider an analytically tractable model of a two level quantum system subject to random shocks and prove that it decays asymptotically to a trivial state, that is, to a state in which the two levels have equal probability of occupation. In a two qubit system, if the shocks affect each qubit independently, the equilibrium density matrix becomes a simple product of the one qubit equilibrium density matrices regardless of the nature of the initial state. This has potential applications to entangles qubits in quantum computers.