some clarification in 8.1

chapter/chapter8.tex

@@ -1,8 +1,7 @@
 %\setcounter{chapter}{7}
 \chapter{Quantum noise and quantum operations}
 \Textbf{8.1}
-Density operator of initial state is written by $\kb{\psi}$ and final state is written by $U\kb{\psi}U^\dagger$.
-Thus time development of $\rho = \kb{\psi}$ can be written by $\mathcal{E}(\rho) = U\rho U^\dagger$.
+State vector identification of the initial state is written as $\ket{\psi}$ and the evolved state is written as $U\ket{\psi} (unitary evolution). In the density operator formalism, $\ket{\psi}$ is identified with $\kb{\psi}$. Thus time development of $\rho = \kb{\psi}$ can be written by $\mathcal{E}(\rho) = U\ket{\psi} (U \ket{\psi})^\dagger = U \kb{\psi} U^\dagger = U \rho U^\dagger$.
 
 \Textbf{8.2}
 From eqn (2.147) (on page 100),