Asymptotic statistical theory of irreducible quantum Markov chains

par Madalin Guta (Nottingham)

mardi 23 juin 2026, 11:15 → 12:15 Europe/Paris

Salle K. Johnson (1R3, 1er étage)

Quantum Markov processes model the dynamics of open quantum systems which are indirectly monitored through continuous time measurements in the environment. This mathematical setup is central to many quantum technology applications such as gravitational wave detectors, quantum magnetometers and atom masers. 

 

In the first part of this talk I will give a brief introduction to some of the key concepts in quantum estimation such as the quantum Cramer-Rao bound and the theory of quantum local asymptotic normality.

 

In the second part of the  talk I will present recent results [1] on the identifiability and asymptotic statistical theory of quantum Markov chains (QMC). On the first topic I will show that the space of identifiable parameters of the stationary output is a stratified space called an orbifold, which is obtained as the quotient of the manifold of irreducible dynamics by a compact group of symmetries. On the second topic, I will show that the joint system–output and reduced output state models converge to a simpler quantum Gaussian shift model and respectively a mixture of Gaussian shifts models build from the tangent space geometric data of the QMC. These  strong convergence results provide the mathematical basis for constructing asymptotically optimal estimators of dynamical parameters. 

 

[1] F. Girotti, J. Kiukas, Madalin Guta, Asymptotic statistical theory of irreducible quantum Markov chains, arXiv:2603.20761.