Statistical properties of Pauli matrices going through noisy channels
Mathematical Physics
2007-12-21 v1 math.MP
Probability
Abstract
We study the statistical properties of the triplet 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.
Keywords
Cite
@article{arxiv.0712.3418,
title = {Statistical properties of Pauli matrices going through noisy channels},
author = {Stéphane Attal and Nadine Guillotin-Plantard},
journal= {arXiv preprint arXiv:0712.3418},
year = {2007}
}