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.
|Number of pages||16|
|Journal||IEEE Transactions on Automatic Control|
|Early online date||07 Jun 2017|
|Publication status||Published - 28 Feb 2018|
- kalman decomposition
- linear quantum systems
FingerprintDive into the research topics of 'The Kalman Decomposition for Linear Quantum Systems'. Together they form a unique fingerprint.
- Faculty of Business and Physcial Sciences, Department of Physics - Personal Chair
Person: Teaching And Research