Miao, ZiboJames, Matthew R.Petersen, Ian R.2016-08-162016-08-160005-1098http://hdl.handle.net/1885/107195The theory of observers is a basic part of classical linear system theory. The purpose of this paper is to develop a theory of coherent observers for linear quantum systems. We provide a class of coherent quantum observers, which track the observables of a linear quantum stochastic system in the sense of mean values, independent of any additional quantum noise in the observer. We prove that there always exists such a coherent quantum observer described by quantum stochastic differential equations in the Heisenberg picture, and show how it can be designed to be consistent with the laws of quantum mechanics. We also find a lower bound for the mean squared estimation error due to the uncertainty principle. In addition, we explore the quantum correlations between a linear quantum plant and the corresponding coherent observer. It is shown that considering a joint plant-observer Gaussian quantum system, entanglement can be generated under the condition that appropriate coefficients of the coherent quantum observer are chosen, and this issue is illustrated in an example. These results pave the way towards observer-based quantum control.We gratefully acknowledge support by the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (project number CE110001027), Australian Research Council Discovery Project (project numbers DP110102322 and DP120101549) and the Air Force Office of Scientific Research (grant numbers FA2386-09-1-4089, FA2386-12- 1-4075 and FA2386-12-1-4084).© 2016 Elsevier LtdQuantum stochastic differential equationsCoherent quantum observersQuantum correlations201610.1016/j.automatica.2016.04.039