The Kalman Decomposition for Linear Quantum Systems

Guofeng Zhang, Symeon Grivopoulos, Ian R. Petersen, John E. Gough

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)

Abstract

This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws of quantum mechanics. We propose a construction method for such transformations that put the system in a Kalman canonical form. Furthermore, we uncover an interesting structure for the obtained decomposition. In the case of passive systems, it is shown that there exist only controllable/observable and uncontrollable/unobservable subsystems. In the general case, controllable/unobservable and uncontrollable/observable subsystems may also be present, but their respective system variables must be conjugate variables of each other. This decomposition naturally exposes decoherence-free modes, quantum-nondemolition modes, quantum-mechanics-free subsystems, and back-action evasion measurements in the quantum system, which are useful resources for quantum information processing, and quantum measurements. The theory developed is applied to physical examples.
Original languageEnglish
Article number7942122
Pages (from-to)331-346
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume63
Issue number2
DOIs
Publication statusPublished - 1 Feb 2018

Keywords

  • Controllability
  • kalman decomposition
  • linear quantum systems
  • observability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this