# Density matrices & spin correlation

1. Dec 9, 2015

### caimzzz

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 $$|\psi > = \frac{1}{\sqrt{2}} ( |+-> - |-+> )$$. The question is: If I measured B and got $$S_{Bz} = 1/2$$. 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:
$$\rho = |\psi><\psi|$$ which is density matrix for A and B. My probability is then $$P = tr ( \rho |-+><-+| )$$ $$\rho = 1/2 ( |+-><+-> - |+-><-+| - |-+><+-| + |-+><-+| )$$.
And then I get: $$P=<-+| \rho |-+> = \frac{1}{2}$$

I think that my equation for probability may me wrong. What should I do?

2. Dec 14, 2015