Limit theorems for Quantum Trajectories

• URL: http://arxiv.org/abs/2302.06191v2
• Date: Wed, 12 Jul 2023 14:44:24 GMT
• Title: Limit theorems for Quantum Trajectories
• Authors: Tristan Benoist, Jan-Luka Fatras, Cl\'ement Pellegrini
• Abstract summary: We prove Law of Large Numbers (LLN), Functional Central Limit Theorem, Law of Iterated Logarithm and Moderate Deviation Principle. Proof of the LLN is based on Birkhoff's ergodic theorem and an analysis of harmonic functions. The other theorems are proved using martingale approximation of empirical sums.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Under purification and irreducibility assumptions, these Markov processes admit a unique invariant measure - see Benoist et al. Probab. Theory Relat. Fields 2019. In this article we prove, finer limit theorems such as Law of Large Numbers (LLN), Functional Central Limit Theorem, Law of Iterated Logarithm and Moderate Deviation Principle. The proof of the LLN is based on Birkhoff's ergodic theorem and an analysis of harmonic functions. The other theorems are proved using martingale approximation of empirical sums.

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