### Abstract

This 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.

Original language | English |
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Pages (from-to) | 263-270 |

Number of pages | 8 |

Journal | Automatica |

Volume | 90 |

DOIs | |

Publication status | Published - 2018 Apr 1 |

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### Keywords

- Cascade realization
- Covariance assignment
- Linear quantum system
- Locally dissipative realization
- Pure Gaussian state

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*Automatica*,

*90*, 263-270. https://doi.org/10.1016/j.automatica.2017.12.061