Hello, I have a question for exercise 2 (c).
The formula in the lecture is : Avg(B_weird) = tr(p_bell * B_weird)
We found both density matrices p_bell and p_stat in (a) and (b).
However I am stuck because I cannot / don't know what is B_weird.
Looking at exercise 1 : I get that A = (+1)|α⟩⟨α| + (−1)|α⊥⟩⟨α⊥|.
So to get B_weird, I get a giant thing that I cannot simplify.
B_weird = A ⊗ B + A ⊗ B ′ − A ′ ⊗ B + A ′ ⊗ B ′
On top of that, I see that the last part of this exercise, we need to plug in the values of alpha, alpha', beta and beta'. Those 4 are scalar values.
α = 0, α ′ = − π / 4 , β = π / 8 , β ′ = − π / 8
How is this possible ? We cannot do cross product of scalars : A = (+1)|α⟩⟨α| + (−1)|α⊥⟩⟨α⊥|
And what about α⊥ ? This one is not even given...
Kind regards,
Thösam
