An application of lifting theory to optical communication processes

Lifting was defined as a continuous mapping from a state space to a bigger one including the original state space and another one. This concept has its background in two mathematical notions, that is, the transition expectation and the compound state. In this sense, lifting can be applied to describe several physical processes and to unify many kinds of state changes. Once a physical process is described by lifting, some complexities such as entropy and mutual entropy can be computed. In this paper, the mathematical structure of quantum channel for optical communication processes is reviewed and it is shown that an attenuation channel can be reconstructed by a lifting expression. Moreover, the process of quantum amplification is expressed by a lifting whose form in state change is more general and useful than the operator expression.