Analysis of Equilibrium Points of Quantum Controlled Dynamics
Naoki Yamamoto, Koji Tsumura, Shinji Hara · Transactions of the Society of Instrument and Control Engineers · 2004
In this paper we investigate some general properties of equilibrium points of finite quantum dynamics which provide fundamental results for designing a controller and a measurement apparatus. Firstly, the averaged quanturn dynamics is shown to be stable in the Lyapunov sense. This implies that the average behavior of the quantum dynamics is characterized by the set of the equilibrium points. Secondly, an explicit form of a unique equilibrium point associated with the controller and the measurement apparatus, which provides a practical procedure to attain a desired equilibrium point, is shown. A quantum state can be utilized as an information source quantified by “von Neumann entropy”. We derive a necessary and sufficient condition for the entropy of the equilibrium points to be maximum (or minimum).