Estimation of Piecewise-Deterministic Trajectories in a Quantum Optics Scenario

Bruno Leggio (1) , Romain Azaïs (1)

1 MOSAIC - Simulation et Analyse de la morphogenèse in siliCo

The manipulation of individual copies of quantum systems is one of the most groundbreaking experimental discoveries in the field of quantum physics. On both an experimental and a theoretical level, it has been shown that the dynamics of a single copy of an open quantum system is a trajectory of a piecewise-deterministic process. To the best of our knowledge, this application field has not been explored by the literature in applied mathematics, from both probabilistic and statistical perspectives. The objective of this chapter is to provide a self-contained presentation of this kind of model, as well as its specificities in terms of observations scheme of the system, and a first attempt to deal with a statistical issue that arises in the quantum world.

Domaines: Physique Quantique [quant-ph]; Statistiques [math.ST]; Probabilités [math.PR]

Bruno Leggio, Romain Azaïs. Estimation of Piecewise-Deterministic Trajectories in a Quantum Optics Scenario. Statistical Topics and Stochastic Models for Dependent Data with Applications, 2020. ⟨hal-02389225⟩