Abstract
We study the statistical properties of the triple (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 triple, which features in the limit a 3-dimensional Brownian motion 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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Attal, S., Guillotin‐Plantard, N. (2009). Statistical properties of Pauli matrices going through noisy channels. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLII. Lecture Notes in Mathematics(), vol 1979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01763-6_16
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DOI: https://doi.org/10.1007/978-3-642-01763-6_16
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