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Density matrices & spin correlation

  1. Dec 9, 2015 #1
    1. The problem statement, all variables and given/known data

    So I have two 1/2 spin systems A and B in a singlet state [tex] |\psi > = \frac{1}{\sqrt{2}} ( |+-> - |-+> ) [/tex]. The question is: If I measured B and got [tex]S_{Bz} = 1/2 [/tex]. What will I measure on state A on z axis?
    2. Relevant equations


    3. The attempt at a solution
    The answer I think is that I will measure spin -1/2 on z axis with probability 1.
    My problem is that I tried to calculate the probability for measuring A on z axis with eigenvalue -1/2 and got probability 1/2. My attempt was:
    [tex] \rho = |\psi><\psi| [/tex] which is density matrix for A and B. My probability is then [tex] P = tr ( \rho |-+><-+| ) [/tex] [tex] \rho = 1/2 ( |+-><+-> - |+-><-+| - |-+><+-| + |-+><-+| ) [/tex].
    And then I get: [tex] P=<-+| \rho |-+> = \frac{1}{2} [/tex]

    I think that my equation for probability may me wrong. What should I do?
     
  2. jcsd
  3. Dec 14, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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