Semiclassical model for a memory dephasing channel

We study a dephasing channel with memory, described by a Hamiltonian model in which the system-environment interaction is described by a stochastic process. We propose a useful way to describe the correlations of channel uses. Moreover, we give a general expression for the coherences decay factors as a function of the number of channel uses and of the stochastic process power spectrum. We also study the impact of memory on the three-qubit code, showing that correlations among channel uses hardly affect the code performance.