Vladimirov, Igor G. (Australian National University), James, Matthew R. (Australian National Univ.), Petersen, Ian R. (Australian National University)

A Karhunen-Loeve Expansion for One-Mode Open Quantum Harmonic Oscillators Using the Eigenbasis of the Two-Point Commutator Kernel

Scheduled for presentation during the Regular Session "Linear Systems and Robust Control" (FA1), Friday, November 29, 2019, 10:15−12:45, WZ Building Room WZ416

2019 Australian & New Zealand Control Conference (ANZCC), November 27-29, 2019, Auckland, New Zealand

This information is tentative and subject to change. Compiled on April 19, 2024

Abstract

This paper considers one-mode open quantum harmonic oscillators with a pair of conjugate position and momentum variables driven by vacuum bosonic fields according to a linear quantum stochastic differential equation. Such systems model cavity resonators in quantum optical experiments. Assuming that the quadratic Hamiltonian of the oscillator is specified by a positive definite energy matrix, we consider a modified version of the quantum Karhunen-Loeve expansion of the system variables proposed recently. The expansion employs eigenvalues and eigenfunctions of the two-point commutator kernel for linearly transformed system variables. We take advantage of the specific structure of this eigenbasis in the one-mode case (including its connection with the classical Ornstein-Uhlenbeck process). These results are applied to computing quadratic-exponential cost functionals which provide robust performance criteria for risk-sensitive control of open quantum systems.