Stability of continuous-time quantum filters

Nina H. Amini (CNRS, Laboratoire des Signaux et Systèmes, France)
June 19, 2015 — 10:30 — "None"

Abstract

In this talk, we study quantum filtering and its stability problem. Indeed, we show that the fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is always a sub-martingale. The observed system could be governed by a continuous-time Stochastic Master Equation (SME), driven simultaneously by Wiener and Poisson processes which takes into account incompleteness and errors in measurements. This stability result is the continuous-time counterpart of a similar stability result already established for discrete-time quantum systems. This result implies the stability of such filtering process but does not necessarily ensure the asymptotic convergence of such quantum filters.

Biography

Nina H. Amini is a CNRS researcher at Laboratory L2S at CentraleSupelec since October 2014. She did her first postdoc from June 2012 for six months at ANU, College of Engineering and Computer Science and her second postdoc at Edward L. Ginzton Laboratory, Stanford University since December 2012. She received her Ph.D. in Mathematics and Control Engineering from Mines-ParisTech (Ecole des Mines de Paris), in September 2012. Prior to her Ph.D., she earned a Master in Financial Mathematics and Statistics at ENSAE and the Engineering Diploma of l’Ecole Polytechnique, in 2009. Her research interests include stochastic control, quantum control, (quantum) filtering theory, (quantum) probability, and (quantum) information theory.