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Limit theorems for quantum trajectories

Author

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  • Benoist, Tristan
  • Fatras, Jan-Luka
  • Pellegrini, Clément

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. (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.

Suggested Citation

  • Benoist, Tristan & Fatras, Jan-Luka & Pellegrini, Clément, 2023. "Limit theorems for quantum trajectories," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 288-310.
    • Handle: RePEc:eee:spapps:v:164:y:2023:i:c:p:288-310
    DOI: 10.1016/j.spa.2023.07.014
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    References listed on IDEAS

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    1. Christine Guerlin & Julien Bernu & Samuel Deléglise & Clément Sayrin & Sébastien Gleyzes & Stefan Kuhr & Michel Brune & Jean-Michel Raimond & Serge Haroche, 2007. "Progressive field-state collapse and quantum non-demolition photon counting," Nature, Nature, vol. 448(7156), pages 889-893, August.
    2. Gao, Fu-Qing, 1996. "Moderate deviations for martingales and mixing random processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 263-275, February.
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