Ma, ShanWoolley, Matthew J.Petersen, IanYamamoto, Naoki2020-01-230005-1098http://hdl.handle.net/1885/199346This paper presents two realizations of linear quantum systems for covariance assignment corresponding to pure Gaussian states. The first one is called a cascade realization; given any covariance matrix corresponding to a pure Gaussian state, we can construct a cascaded quantum system generating that state. The second one is called a locally dissipative realization; given a covariance matrix corresponding to a pure Gaussian state, if it satisfies certain conditions, we can construct a linear quantum system that has only local interactions with its environment and achieves the assigned covariance matrix. Both realizations are illustrated by examples from quantum optics.This work was supported by the 111 Project (B17048), the Australian Research Council (ARC) under grant FL110100020, the Air Force Office of Scientific Research (AFOSR), under agreement number FA2386-16-1-4065, the Australian Academy of Science, and JSPS Grant-in-Aid No. 15K06151.application/pdfen-AU© 2018 Elsevier LtdLinear quantum systemCascade realizationLocally dissipative realizationCovariance assignmentPure Gaussian state2018-02-1510.1016/j.automatica.2017.12.0612019-11-25