Quantum Channel, and Information Quantity, and Their Mathematical Structure

Abstract

Any quantum operation can be regarded as a quantum channel by considering that the initial and final states are the input and output state, respectively. That is, they are the mathematically same object. In this book, for a unified treatment, we use only the term quantum channel. Especially, the main purpose of quantum theory is the precise prediction (description) of the change of the state due to the time evolution in several environments. In the following, we define a quantum channel as a map from an input state to an output state, and this definition brings the mathematically completed framework to satisfy the above purpose. We also discuss information quantities of the quantum system and its relation with quantum channel.