Open quantum systems with linear dynamics: optimal unravellings for optimal feedback control

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Title Open quantum systems with linear dynamics: optimal unravellings for optimal feedback control
Author Wiseman, Howard Mark; Doherty, Andrew C.
Publication Title Fluctuations and noise in photonics and quantum optics II. SPIE proceedings 5468
Editor Heszler, P.
Year Published 2004
Place of publication Bellingham, WA, USA
Publisher SPIE
Abstract Quantum feedback control is the control of the dynamics of a quantum system by feeding back (in real time) the results of monitoring that system. For systems with linear dynamics, the control problem is amenable to exact analysis. In these cases, the quantum system is equivalent to a stochastic system of classical phase-space variables with linear drift and constant diffusion, and with a measured current (e.g. a homodyne photocurrent) linear in the system variables. However, the classical evolution is constrained in order to represent valid quantum evolution. We quantify this in terms of a linear matrix inequality (LMI) relating the drift and diffusion (a sort of zero temperature fluctuation-dissipation theorem), and another LMI for the covariance matrix of the possible conditioned states (i.e. under all possible monitoring schemes consistent with the master equation). For manipulable systems (i.e. where the experimenter has arbitrary control over the parameters in a Hamiltonian linear in the system variables) the covariance of the conditioned state is all that is needed to calculate the effectiveness of the feedback. In this case the double optimization problem reduces to a semidefinite program, which can be solved efficiently in general. We illustrate this with an example drawn from quantum optics.
Peer Reviewed Yes
Published Yes
Publisher URI http://spiedl.org/dbt/dbt.jsp?KEY=PSISDG&Volume=5468&Issue=1&bproc=symp&scode=FN04
Alternative URI http://ttp://dx.doi.org/10.1117/12.547492
Copyright Statement Copyright 2004 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.
ISBN 0819453919
Conference name Fluctuations and noise in photonics and quantum optics II.
Location Maspalomas, Spain
Date From 2004-05-26
Date To 2004-05-28
Date Accessioned 2009-07-27
Date Available 2009-10-13T21:52:22Z
Language en_AU
Research Centre Centre for Quantum Dynamics
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Quantum Physics
Publication Type Conference Publications (Full Written Paper - Refereed)
Publication Type Code e1a

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