Contraction rates for quantum exclusion semigroups in Wasserstein-1 distance
Abstract
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.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Quantum Mechanics and Applications
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Stochastics
- Volume
- 98
- Issue
- 6
- Pages
- 861–882
- Publication date
- 11 February 2026
- Language
- EN