2,655 research outputs found
Quantum filtering for multiple input multiple output systems driven by arbitrary zero-mean jointly Gaussian input fields
In this paper, we treat the quantum filtering problem for multiple input
multiple output (MIMO) Markovian open quantum systems coupled to multiple boson
fields in an arbitrary zero-mean jointly Gaussian state, using the reference
probability approach formulated by Bouten and van Handel as a quantum version
of a well-known method of the same name from classical nonlinear filtering
theory, and exploiting the generalized Araki-Woods representation of Gough.
This includes Gaussian field states such as vacuum, squeezed vacuum, thermal,
and squeezed thermal states as special cases. The contribution is a derivation
of the general quantum filtering equation (or stochastic master equation as
they are known in the quantum optics community) in the full MIMO setup for any
zero-mean jointy Gaussian input field states, up to some mild rank assumptions
on certain matrices relating to the measurement vector.Comment: 19 pages, no figures. Published in a special issue of the Russian
Journal of Mathematical Physics dedicated to the memory of Slava Belavki
Quantum filtering for multiple measurements driven by fields in single-photon states
In this paper, we derive the stochastic master equations for quantum systems
driven by a single-photon input state which is contaminated by quantum vacuum
noise. To improve estimation performance, quantum filters based on
multiple-channel measurements are designed. Two cases, namely diffusive plus
Poissonian measurements and two diffusive measurements, are considered.Comment: 8 pages, 6 figures, submitted for publication. Comments are welcome
A Phase-space Formulation of the Belavkin-Kushner-Stratonovich Filtering Equation for Nonlinear Quantum Stochastic Systems
This paper is concerned with a filtering problem for a class of nonlinear
quantum stochastic systems with multichannel nondemolition measurements. The
system-observation dynamics are governed by a Markovian Hudson-Parthasarathy
quantum stochastic differential equation driven by quantum Wiener processes of
bosonic fields in vacuum state. The Hamiltonian and system-field coupling
operators, as functions of the system variables, are represented in a Weyl
quantization form. Using the Wigner-Moyal phase-space framework, we obtain a
stochastic integro-differential equation for the posterior quasi-characteristic
function (QCF) of the system conditioned on the measurements. This equation is
a spatial Fourier domain representation of the Belavkin-Kushner-Stratonovich
stochastic master equation driven by the innovation process associated with the
measurements. We also discuss a more specific form of the posterior QCF
dynamics in the case of linear system-field coupling and outline a Gaussian
approximation of the posterior quantum state.Comment: 12 pages, a brief version of this paper to be submitted to the IEEE
2016 Conference on Norbert Wiener in the 21st Century, 13-15 July, Melbourne,
Australi
Robust quantum parameter estimation: coherent magnetometry with feedback
We describe the formalism for optimally estimating and controlling both the
state of a spin ensemble and a scalar magnetic field with information obtained
from a continuous quantum limited measurement of the spin precession due to the
field. The full quantum parameter estimation model is reduced to a simplified
equivalent representation to which classical estimation and control theory is
applied. We consider both the tracking of static and fluctuating fields in the
transient and steady state regimes. By using feedback control, the field
estimation can be made robust to uncertainty about the total spin number
Lyapunov Stability Analysis for Invariant States of Quantum Systems
In this article, we propose a Lyapunov stability approach to analyze the
convergence of the density operator of a quantum system. In contrast to many
previously studied convergence analysis methods for invariant density operators
which use weak convergence, in this article we analyze the convergence of
density operators by considering the set of density operators as a subset of
Banach space. We show that the set of invariant density operators is both
closed and convex, which implies the impossibility of having multiple isolated
invariant density operators. We then show how to analyze the stability of this
set via a candidate Lyapunov operator.Comment: A version of this paper has been accepted at 56th IEEE Conference on
Decision and Control 201
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