Transfer function approach to quantum Control-Part II: Control concepts and applications

Based on the stochastic differential equation of quantum mechanical feedback obtained in the first part of this paper, detailed control concepts and applications are discussed for quantum systems interacting with a noncommutative noise source. A feedback system in our framework is purely nonclassical in the sense that feedback control is performed via local operation and quantum communication through a quantum channel. The role of the controller is to alter the quantum dynamic characteristics of the plant through entanglement, shared between the plant and controller by sending quantum states, that is modulated by the Hamiltonian on the controller. The input-output relation of quantum systems provides a natural extension of control theory to the quantum domain. This enables one to present a control theoretical interpretation of some fundamental quantum mechanical notions such as the uncertainty principle, but also to find applications of ideas and tools of control theory. One of the most important applications is the production of squeezed states, which has been an important issue of quantum theory in relation to quantum computation and quantum communication. The method proposed here reduces the application to a conventional noise reduction problem with feedback. The H_∞ control then leads to complete squeezing.