- #1
ma18
- 93
- 1
Homework Statement
Consider the bipartite observable
O_AB = (sigma_A · n) ⊗ (sigma_B · m)
Where n and m are three vectors and
sigma_i = (sigma_1_i, sigma_2_i, sigma_3_i)
with i = [A,B] are the Pauli vectors.
Compute using abstract and matrix representation the expectation value of O_AB in the Bell State
|ψ> = 1/sqrt(2) (|0_A 1_B> +|1_A 0_B))
for n = (0,1,0)† , b = (0,0,1)†
The Attempt at a Solution
Alright so first I computed the representation of the observable
Applying the values of n and m it comes to
O_AB = sigma_2_A ⊗ sigma_3_B
= (0 -i ⊗ (1 0
i 0) 0 -1)
= (0 0 -i 0
0 0 0 1
i 0 0 0
0 -i 0 0)
After this I am not sure how to proceed with calculating the expectation value as I don't know how to represent
|ψ> = 1/sqrt(2) (|0_A 1_B> +|1_A 0_B))
as a matrix
Any help would be much appreciated!