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SUMMARY:Asymptotic statistical theory of irreducible quantum Markov chains
DTSTART:20260623T091500Z
DTEND:20260623T101500Z
DTSTAMP:20260810T225900Z
UID:indico-event-14487@indico.math.cnrs.fr
DESCRIPTION:Speakers: Madalin Guta (Nottingham)\n\nQuantum Markov processe
 s model the dynamics of open quantum systems which are indirectly monitore
 d through continuous time measurements in the environment. This mathematic
 al setup is central to many quantum technology applications such as gravi
 tational wave detectors\, quantum magnetometers and atom masers. \n \nIn
  the first part of this talk I will give a brief introduction to some of t
 he key concepts in quantum estimation such as the quantum Cramer-Rao bound
  and the theory of quantum local asymptotic normality.\n \nIn the second 
 part of the  talk I will present recent results [1] on the identifiabilit
 y 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 obta
 ined 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 syst
 em–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 con
 vergence results provide the mathematical basis for constructing asymptoti
 cally optimal estimators of dynamical parameters. \n \n[1] F. Girotti\, 
 J. Kiukas\, Madalin Guta\, Asymptotic statistical theory of irreducible qu
 antum Markov chains\, arXiv:2603.20761.\n\nhttps://indico.math.cnrs.fr/eve
 nt/14487/
LOCATION:Salle K. Johnson (1R3\, 1er étage)
URL:https://indico.math.cnrs.fr/event/14487/
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