Contraction rates for quantum exclusion semigroups in Wasserstein-1 distance

The quantum exclusion semigroup constructed from quantum Bernoulli noise decomposes into distinct actions on diagonal and off-diagonal operator spaces. Its restriction to the diagonal subspace corresponds to a classical Markov process. In this paper, we establish explicit contraction rates for this semigroup under the Wasserstein-1 distance. For arbitrary initial states, the Wasserstein distance between evolved states decays exponentially with a rate combining the Wasserstein curvature of the classical Markov process and the decay rate of quantum off-diagonal operators. The contraction features a prefactor constant containing a quantum correction term that quantifies how coherence affects the convergence dynamics.