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QM: Purity, two-outcome measurements

  1. Nov 13, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-11-13_23-44-34.png

    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
    upload_2017-11-13_23-49-1.png

    upload_2017-11-13_23-49-37.png

    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. :smile:
     
  2. jcsd
  3. Nov 14, 2017 #2

    DrClaude

    User Avatar

    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.
     
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