63 research outputs found
Quantum risk-sensitive estimation and robustness
This paper studies a quantum risk-sensitive estimation problem and
investigates robustness properties of the filter. This is a direct extension to
the quantum case of analogous classical results. All investigations are based
on a discrete approximation model of the quantum system under consideration.
This allows us to study the problem in a simple mathematical setting. We close
the paper with some examples that demonstrate the robustness of the
risk-sensitive estimator.Comment: 24 page
Stochastic Schrodinger equations
A derivation of stochastic Schrodinger equations is given using quantum
filtering theory. We study an open system in contact with its environment, the
electromagnetic field. Continuous observation of the field yields information
on the system: it is possible to keep track in real time of the best estimate
of the system's quantum state given the observations made. This estimate
satisfies a stochastic Schrodinger equation, which can be derived from the
quantum stochastic differential equation for the interaction picture evolution
of system and field together. Throughout the paper we focus on the basic
example of resonance fluorescence.Comment: 24 page
Filtering and Control in Quantum Optics
In this thesis we study continuously observed open quantum systems from the
point of view of quantum filtering theory. The conditioned state of the open
system obeys a non-commutative or quantum analogue of the Kushner-Stratonovich
equation in classical filtering theory. The thesis consists out of four
chapters. The first chapter is a brief introduction to quantum probability
theory and quantum stochastic calculus. The second chapter is a description of
a photon counting experiment in continuous time within the framework of Davies
and Srinivas. The third chapter focusses on the derivation of the quantum
filtering or Belavkin equation from the quantum stochastic differential
equation governing the interaction between the open system and its environment,
the electromagnetic field. The fourth chapter shows how the quantum filtering
equation can be used to control quantum systems.Comment: PhD thesis, University of Nijmegen, 200
Approximation and limit theorems for quantum stochastic models with unbounded coefficients
We prove a limit theorem for quantum stochastic differential equations with
unbounded coefficients which extends the Trotter-Kato theorem for contraction
semigroups. From this theorem, general results on the convergence of
approximations and singular perturbations are obtained. The results are
illustrated in several examples of physical interest.Comment: 23 page
An introduction to quantum filtering
This paper provides an introduction to quantum filtering theory. An
introduction to quantum probability theory is given, focusing on the spectral
theorem and the conditional expectation as a least squares estimate, and
culminating in the construction of Wiener and Poisson processes on the Fock
space. We describe the quantum It\^o calculus and its use in the modelling of
physical systems. We use both reference probability and innovations methods to
obtain quantum filtering equations for system-probe models from quantum optics.Comment: 41 pages, 1 figur
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