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

• URL: http://arxiv.org/abs/2303.08992v1
• Date: Wed, 15 Mar 2023 23:49:56 GMT
• Title: Law of large numbers and central limit theorem for ergodic quantum processes
• Authors: Lubashan Pathirana and Jeffrey Schenker
• Abstract summary: A discrete quantum process is represented by a sequence of quantum operations. We consider quantum processes that are obtained by repeated iterations of a quantum operation with noise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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