Exercise 7.6

Eq. 7.22 in the textbook is: \[ P(a) = \rho_{aa} \]

The probability to get \(a\) is the diagonal element \(aa\) of the density matrix.

According to the rules of probability, the sum over all probabilities \(P(a)\) equals to 1:

\[ \sum_a P(a) = 1 \Rightarrow \sum_a \rho_{aa} = 1 \Rightarrow \mathrm{Tr} (\rho) = 1 \]