The Kalman decomposition for Linear Quantum Stochastic Systems

Grivopoulos, Symeon; Petersen, Ian R.; Gough, John E.

doi:10.23919/acc.2017.7963095

Cited by 5 publications

(3 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It follows from the form of the matrix H in (15) that the "h" subsystem (11), in general, interacts with the "co" subsystem (12) and "cō" subsystem (10) via the sub-matrices H 12 and H 13 , respectively. As far as the Kalman canonical form is concerned, the sub-matrices H 12 and H 13 are free parameters; see also the interconnections among subsystems in Fig.…”

Section: A Refinement Of the Quantum Kalman Canonical Formmentioning

confidence: 99%

“…Indeed, the system in Example 5.4 below can be decomposed into two invariant co subsystems, each of which is a harmonic oscillator driven by a single input field. It is interesting to see that the subsystem G m is in the Kalman canonical form (6), while G cō , G h , and G co are in the form of ( 10), (11), and ( 12) respectively. Therefore, the quantum Kalman canonical form ( 6) is decomposed into four subsystems which are decoupled from each other, and one of which itself is a smaller Kalman canonical form.…”

Section: A Refinement Of the Quantum Kalman Canonical Formmentioning

confidence: 99%

“…In [47], the quantities x co , x cō , q h , p h are used to denote the quadrature operators of the co, cō, cō, co subsystems respectively. The Kaman canonical form has also been derived in Reference [11] by means of an SVD-like factorization.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Structural Characterization of Linear Quantum Systems With Application to Back-Action Evading Measurement

Petersen

2020

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

The purpose of this paper is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper [47]. The spectral structure of quantum linear systems is explored, which indicates that a quantum linear system is both controllable and observable provided that it is Hurwitz stable. A new parameterization method for quantum linear systems is proposed. This parameterization is designed for the Kalman canonical form directly. Consequently, the parameters involved are in a blockwise form in correspondence with the blockwise structure of the Kalman canonical form. This parameter structure can be used to simplify various quantum control design problems. For example, necessary and sufficient conditions for the realization of quantum back-action evading (BAE) measurements are given in terms of these new parameters. Due to their blockwise nature, a small number of parameters are required for realizing quantum BAE measurements.Index Terms-Quantum linear systems; Kalman canonical form; back-action evading (BAE) measurements. −A 12, and C co1 = V m3Γco1 , Based on Lemmas 3.7-3.9 and the subsystem G m given in (28), we are now in a position to propose the following result.

show abstract

Section: A Refinement Of the Quantum Kalman Canonical Formmentioning

confidence: 99%

Section: A Refinement Of the Quantum Kalman Canonical Formmentioning

confidence: 99%