Bounded Real Properties for a Class of Annihilation-Operator Linear Quantum Systems

This paper considers the bounded real properties for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. The paper considers complex quantum versions of the Bounded Real Lemma, the Strict Bounded Real Lemma and the Lossless Bounded Real Lemma. For the class of quantum systems under consideration, it is shown that the question of physical realizability is related to the Bounded Real and Lossless Bounded Real properties.