# QM: Purity, two-outcome measurements

Tags:
1. Nov 13, 2017

### alc95

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.

2. Nov 14, 2017

### Staff: Mentor

In Q1, you didn't specify what $|x_k \rangle$ is.

For Q2, just go step by step, either by replacing the density operator for its bracket representation then taking the trace, or the other way around.