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arXiv · 2303.08992

Law of large numbers and central limit theorem for ergodic quantum processes

Lubashan Pathirana·Jeffrey Schenker
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Abstract

A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum operation with noise. Such ergodic quantum processes generalize independent quantum processes. An ergodic theorem describing convergence to equilibrium for a general class of such processes was recently obtained by Movassagh and Schenker. Under irreducibility and mixing conditions, we obtain a central limit type theorem describing fluctuations around the ergodic limit.

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Lubashan Pathirana, Jeffrey Schenker. 2023-03-15. Law of large numbers and central limit theorem for ergodic quantum processes. https://doi.org/10.1063/5.0153483

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