A karhunen-loeve expansion for one-mode open quantum harmonic oscillators using the eigenbasis of the two-point commutator kernel

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    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.

    Original languageEnglish
    Title of host publication2019 Australian and New Zealand Control Conference, ANZCC 2019
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages179-184
    Number of pages6
    ISBN (Electronic)9781728117867
    DOIs
    Publication statusPublished - Nov 2019
    Event2019 Australian and New Zealand Control Conference, ANZCC 2019 - Auckland, New Zealand
    Duration: 27 Nov 201929 Nov 2019

    Publication series

    Name2019 Australian and New Zealand Control Conference, ANZCC 2019

    Conference

    Conference2019 Australian and New Zealand Control Conference, ANZCC 2019
    Country/TerritoryNew Zealand
    CityAuckland
    Period27/11/1929/11/19

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