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SUMMARY:Irreducibility in Gaussian Quantum Markov Semigroups
DTSTART:20260625T090000Z
DTEND:20260625T100000Z
DTSTAMP:20260809T200300Z
UID:indico-event-16580@indico.math.cnrs.fr
DESCRIPTION:Speakers: Federico Girotti (Politecnico di Milano)\n\nGaussian
  Quantum Markov Semigroups (GQMSs) constitute the class of all Markovian e
 volutions of bosonic systems that map quantum Gaussian states into quantum
  Gaussian states. They first appeared in the physics literature in the stu
 dy of reduced evolutions of bosonic systems governed by quadratic Hamilton
 ians and interacting linearly with bosonic fields. Such models efficiently
  describe a wide range of experiments in quantum optics and correspond to 
 operations that can be realistically implemented in the laboratory.\nBesid
 es their physical relevance\, there are strong mathematical motivations fo
 r the study of GQMSs. Indeed\, these semigroups possess a remarkably rich 
 mathematical structure\, allowing for a detailed understanding of many asp
 ects of their dynamics\, as in the case of their classical counterparts\, 
 namely Ornstein–Uhlenbeck semigroups. In the case of finitely many modes
 \, the evolution is described by finitely many parameters\, and several pr
 oblems can be reformulated in linear-algebraic terms.\nDespite the ubiquit
 y of quantum Gaussian evolutions in the literature\, their rigorous mathem
 atical understanding remains less developed than that of their classical c
 ounterparts. Even in the finite-dimensional case\, the quantum framework p
 resents several additional challenges arising from its richer structure. N
 evertheless\, there has been growing interest in the rigorous analysis of 
 GQMSs in recent years\, leading to a number of significant advances.\nIn t
 his talk\, we will focus on the study of irreducibility for GQMSs. When a 
 normal invariant state exists\, the structure of the semigroup turns out t
 o be remarkably rigid\, and the reducibility problem can be successfully a
 ddressed through the analysis of the set of normal invariant states. By co
 ntrast\, the general case requires different techniques. We will show how 
 the study of regularisation properties of the semigroup leads to a charact
 erisation of irreducibility in terms of simple conditions on the parameter
 s defining the evolution.\n\nhttps://indico.math.cnrs.fr/event/16580/
LOCATION:Huron (106) (Bât. 1R1)
URL:https://indico.math.cnrs.fr/event/16580/
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