QM: Purity, two-outcome measurements

[alc95]

Homework Statement

Homework 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)

The Attempt at a Solution

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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.

 

[DrClaude]

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.