Figure 3

The redundancy vs. time for Gaussian decoherence with an initially pure environment.

Here, the couplings are chosen uniformly from the interval [−2, 2], which gives . The other parameters are p_↑ = 1/2 and δ = 10⁻¹⁶. The blue squares are from computing the Holevo quantity with very large environments and the black line is the QCB result, Eq. (29). The green star is the redundancy onset time, Eq. (30). The three black dashed lines are for different finite (for a fixed realization of the random coupling constants). For finite environments, there is a quadratic growth of the redundancy up to the recurrence time, , where information flows from the environment back into the system. The recurrence time for each of the finite environments is indicated by the black dotted lines. Thus, even for finite environments, one can expect to see signatures of Gaussian behavior in the redundancy.