### 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 |

### Fingerprint

### 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

**Cascade and locally dissipative realizations of linear quantum systems for pure Gaussian state covariance assignment.** / Ma, Shan; Woolley, Matthew J.; Petersen, Ian R.; Yamamoto, Naoki.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Cascade and locally dissipative realizations of linear quantum systems for pure Gaussian state covariance assignment

AU - Ma, Shan

AU - Woolley, Matthew J.

AU - Petersen, Ian R.

AU - Yamamoto, Naoki

PY - 2018/4/1

Y1 - 2018/4/1

N2 - 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.

AB - 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.

KW - Cascade realization

KW - Covariance assignment

KW - Linear quantum system

KW - Locally dissipative realization

KW - Pure Gaussian state

UR - http://www.scopus.com/inward/record.url?scp=85041389835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041389835&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2017.12.061

DO - 10.1016/j.automatica.2017.12.061

M3 - Article

AN - SCOPUS:85041389835

VL - 90

SP - 263

EP - 270

JO - Automatica

JF - Automatica

SN - 0005-1098

ER -