English

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 (σx,σy,σz)(\sigma_x,\sigma_y,\sigma_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.

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}
}