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 being occupied. 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 matrix, regardless of the form of the initial state. This has potential applications to entangled qubits in quantum computers.