1. The problem statement, all variables and given/known data 2. Relevant equations in addition to those provided in the questions, I used the following: Tr(B) = sigma<x_j|B|x_j> purity = Tr(rho^2) 3. The attempt at a solution I find calculating trace and purity very confusing. Am I on the right track with question 1? With question 2, I am really unsure about how to proceed further. Any help would be greatly appreciated. Thanks in advance.