2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144658We study the statistical properties of the triplet $(σ_x,σ_y,σ_z)$ of Pauli matrices going through a sequence of noisy channels, modeled by the repetition of a general, trace-preserving, completely positive map. We show a non-commutative central limit theorem for the distribution of this triplet, which shows up a 3-dimensional Brownian motion in the limit with a non-trivial covariance matrix. We also prove a large deviation principle associated to this convergence, with an explicit rate function depending on the stationary state of the noisy channel.Mathematical PhysicsProbabilitytext