TY - JOUR
T1 - Structural Characterization of Linear Quantum Systems with Application to Back-Action Evading Measurement
AU - Zhang, Guofeng
AU - Petersen, Ian R.
AU - Li, Jinghao
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2020/7
Y1 - 2020/7
N2 - The purpose of this article is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper. 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.
AB - The purpose of this article is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper. 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.
KW - Back-action evading (BAE) measurements
KW - Kalman canonical form
KW - quantum linear systems
UR - http://www.scopus.com/inward/record.url?scp=85087513925&partnerID=8YFLogxK
U2 - 10.1109/TAC.2019.2946234
DO - 10.1109/TAC.2019.2946234
M3 - Article
SN - 0018-9286
VL - 65
SP - 3157
EP - 3163
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 7
M1 - 8862949
ER -