Coherent-Classical Estimation for Quantum Linear Systems

This paper introduces a problem of coherent-classical estimation for a class of linear quantum systems. In this problem, the estimator is a mixed quantum-classical system which produces a classical estimate of a system variable. The coherent-classical estimator may also involve coherent feedback. An example involving optical squeezers is given to illustrate the efficacy of this idea.Comment: A version of this paper will appear in the Proceedings of the 2013 Australian Control Conferenc

Coherent-Classical Estimation versus Purely-Classical Estimation for Linear Quantum Systems

We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comprises an estimator that is a mixed quantum-classical system without involving coherent feedback. The estimator yields a classical estimate of a variable for the quantum plant. We demonstrate that for a passive plant that can be characterized by annihilation operators only, such coherent-classical estimation provides no improvement over purely-classical estimation. An example is also given which shows that if the plant is not assumed to be an annihilation operator only quantum system, it is possible to get better estimates with such coherent-classical estimation compared with purely-classical estimation.Comment: 7 pages, 5 figures. Minor corrections. Accepted, 2014 Conference on Decision and Contro

Coherent-classical estimation for linear quantum systems

We study a coherent-classical estimation scheme for a class of linear quantum systems, where the estimator is a mixed quantum–classical system that may or may not involve coherent feedback. We show that when the quantum plant or the quantum part of the estimator (coherent controller) is an annihilation operator only system, coherent-classical estimation without coherent feedback can provide no improvement over purely-classical estimation. Otherwise, coherent-classical estimation without feedback can be better than classical-only estimation for certain homodyne detector angles, although the former is inferior to the latter for the best choice of homodyne detector angle. Moreover, we show that coherent-classical estimation with coherent feedback is no better than classical-only estimation, when both the plant and the coherent controller are annihilation operator only systems. Otherwise, coherent-classical estimation with coherent feedback can be superior to purely-classical estimation, and in this case, the former is better than the latter for the optimal choice of homodyne detector angle.This work was supported by the Australian Research Council (ARC) under grants CE110001027 (EHH) and FL110100020 (IRP), and by the US Air Force Office of Scientific Research (AFOSR) under agreement number FA2386-16-1-4065 (IRP). SR was funded by the Singapore National Research Foundation Grant No. NRFNRFF2011-07 and the Singapore Ministry of Education Academic Research Fund Tier 1 Project R-263-000-C06-112, and is currently funded by the UK National Quantum Technologies Programme (EP/M01326X/1, EP/M013243/1

Robust H∞ Coherent-Classical Estimation of Linear Quantum Systems

We study robust H∞ coherent-classical estimation for a class of physically realizable linear quantum systems with parameter uncertainties. Such a robust coherent-classical estimator, with or without coherent feedback, can yield better disturbance-to-error performance than the corresponding robust purely-classical estimator for an uncertain plant. Moreover, coherent feedback allows for such a robust coherent-classical estimator to be more robust to uncertainty in comparison to the robust classical-only estimator.This work was supported by the Australian Research Council and the Singapore National Research Foundation