23 research outputs found
Directly Coupled Observers for Quantum Harmonic Oscillators with Discounted Mean Square Cost Functionals and Penalized Back-action
This paper is concerned with quantum harmonic oscillators consisting of a
quantum plant and a directly coupled coherent quantum observer. We employ
discounted quadratic performance criteria in the form of exponentially weighted
time averages of second-order moments of the system variables. A coherent
quantum filtering (CQF) problem is formulated as the minimization of the
discounted mean square of an estimation error, with which the dynamic variables
of the observer approximate those of the plant. The cost functional also
involves a quadratic penalty on the plant-observer coupling matrix in order to
mitigate the back-action of the observer on the covariance dynamics of the
plant. For the discounted mean square optimal CQF problem with penalized
back-action, we establish first-order necessary conditions of optimality in the
form of algebraic matrix equations. By using the Hamiltonian structure of the
Heisenberg dynamics and related Lie-algebraic techniques, we represent this set
of equations in a more explicit form in the case of equally dimensioned plant
and observer.Comment: 11 pages, a brief version to be submitted to the IEEE 2016 Conference
on Norbert Wiener in the 21st Century, 13-15 July, Melbourne, Australi
A transverse Hamiltonian variational technique for open quantum stochastic systems and its application to coherent quantum control
This paper is concerned with variational methods for nonlinear open quantum
systems with Markovian dynamics governed by Hudson-Parthasarathy quantum
stochastic differential equations. The latter are driven by quantum Wiener
processes of the external boson fields and are specified by the system
Hamiltonian and system-field coupling operators. We consider the system
response to perturbations of these energy operators and introduce a transverse
Hamiltonian which encodes the propagation of the perturbations through the
unitary system-field evolution. This provides a tool for the infinitesimal
perturbation analysis and development of optimality conditions for coherent
quantum control problems. We apply the transverse Hamiltonian variational
technique to a mean square optimal coherent quantum filtering problem for a
measurement-free cascade connection of quantum systems.Comment: 12 pages, 1 figure. A brief version of this paper will appear in the
proceedings of the IEEE Multi-Conference on Systems and Control, 21-23
September 2015, Sydney, Australi
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
Advances in Quantum Theory
The quantum theory is the first theoretical approach that helps one to successfully understand the atomic and sub-atomic worlds which are too far from the cognition based on the common intuition or the experience of the daily-life. This is a very coherent theory in which a good system of hypotheses and appropriate mathematical methods allow one to describe exactly the dynamics of the quantum systems whose measurements are systematically affected by objective uncertainties. Thanks to the quantum theory we are able now to use and control new quantum devices and technologies in quantum optics and lasers, quantum electronics and quantum computing or in the modern field of nano-technologies