Physical realizability conditions for mixed bilinear-linear quantum cascades with pure field coupling

Author

Duffaut Espinosa, Luis A. ; Miao, Zhenjiang ; Petersen, Ian R. ; Ugrinovskii, V. ; James, Michael R.

Author_Institution

Sch. of Eng. & Inf. Technol., Univ. of New South Wales at ADFA, Canberra, ACT, Australia

fYear

2013

fDate

10-13 Dec. 2013

Firstpage

1866

Lastpage

1871

Abstract

This paper aims to provide conditions under which a quantum stochastic differential equation can serve as a model for interconnection of a bilinear system evolving on an operator group SU(2) and a linear quantum system representing a quantum harmonic oscillator. To answer this question we derive algebraic conditions for the preservation of canonical commutation relations (CCRs) of quantum stochastic differential equations (QSDE) having a subset of system variables satisfying the harmonic oscillator CCRs, and the remaining variables obeying the CCRs of SU(2). Then, it is shown that from the physical realizability point of view such QSDEs correspond to bilinear-linear quantum cascades.

Keywords

bilinear systems; cascade systems; differential equations; discrete time systems; harmonic oscillators; linear systems; mathematical operators; nonlinear control systems; quantum theory; QSDE; SU(2) operator group; algebraic conditions; bilinear system interconnection model; canonical commutation relations preservation; linear quantum system; mixed bilinear-linear quantum cascades; physical realizability conditions; pure field coupling; quantum harmonic oscillator; quantum stochastic differential equation; Couplings; Harmonic analysis; Mathematical model; Noise; Oscillators; Quantum mechanics; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on

Conference_Location

Firenze

ISSN

0743-1546

Print_ISBN

978-1-4673-5714-2

Type

conf

DOI

10.1109/CDC.2013.6760154

Filename

6760154