Statistical properties of Pauli matrices going through noisy channels

Details Statistical properties of Pauli matrices going through noisy channels Statistical properties of Pauli matrices going through noisy channels

2007-12-20

arxiv.org/abs/0712.3418v1

Physics

Mathematical Physics

Scientific paper

We study the statistical properties of the triplet $(\sigma_x,\sigma_y,\sigma_z)$ 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.

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