Statistical properties of Pauli matrices going through noisy channels
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Niveau: Supérieur, Doctorat, Bac+8
Statistical properties of Pauli matrices going through noisy channels Stephane Attal and Nadine Guillotin-Plantard ? June 24, 2008 Abstract We study the statistical properties of the triplet (?x, ?y, ?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. 1 Introduction In quantum information theory one of the most important question is to un- derstand and to control the way a quantum bit is modified when transmitted through a quantum channel. It is well-known that realistic transmission channels are not perfect and that they distort the quantum bit they trans- mit. This transformation of the quantum state is represented by the action of a completely positive map. These are the so-called noisy channels. The purpose of this article is to study the action of the repetition of a general completely positive map on basic observables. Physically, this model can be thought of as the sequence of transformations of small identical ?Universite de Lyon, Universite Lyon 1, Institut Camille Jordan, U.
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Statistical properties of Pauli matrices going through noisy channels Stephane Attal and Nadine Guillotin-Plantard ? June 24, 2008 Abstract We study the statistical properties of the triplet (?x, ?y, ?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. 1 Introduction In quantum information theory one of the most important question is to un- derstand and to control the way a quantum bit is modified when transmitted through a quantum channel. It is well-known that realistic transmission channels are not perfect and that they distort the quantum bit they trans- mit. This transformation of the quantum state is represented by the action of a completely positive map. These are the so-called noisy channels. The purpose of this article is to study the action of the repetition of a general completely positive map on basic observables. Physically, this model can be thought of as the sequence of transformations of small identical ?Universite de Lyon, Universite Lyon 1, Institut Camille Jordan, U.
- dimensional brownian
- king-ruskai-szarek-werner repre- sentation
- large devia- tion principle
- positive map
- quantum random
- walk associ- ated
- know quantum channels
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