Qubit dynamics with classical noise

Abstract

We study the evolution of a qubit evolving according to the Schrödinger equation with a Hamiltonian containing noise terms, modeled by random diagonal and offdiagonal matrix elements. We show that the noise-averaged qubit density matrix converges to a final state, in the limit of large times t. The convergence speed is polynomial in 1/t, with a power depending on the regularity of the noise probability density and its low frequency behaviour. We evaluate the final state explicitly. We show that in the regimes of weak and strong off-diagonal noise, the process implements the dephasing channel in the energy-(localized) and the delocalized basis, respectively.