Problem 2 (7 pt)
Assume Charlie has prepared the two spins in the singlet state |s:| and sends them to Alice and Bob to measure.
(a) If Alice measures σ(z) and Bob measures τ(z), what is the expectation value of σ(z)τ(z)?
(b) If Alice measures σ(x) and Bob measures τ(x), what is the expectation value of σ(x)τ(x)?
(c) If Alice measures σ(y) and Bob measures τ(y), what is the expectation value of σ(y)τ(y)?
(d) If Alice measures σ(x) and Bob measures τ(y), what is the expectation value of σ(x)τ(y)?
Now assume Charlie instead prepares the two spins in the so-called triplet state |T₁:| and sends them to Alice and Bob to measure.
(e) If Alice measures σ(z) and Bob measures τ(z), what is the expectation value of σ(z)τ(z)?
(f) If Alice measures σ(x) and Bob measures τ(x), what is the expectation value of σ(x)τ(x)?
(g) If Alice measures σ(y) and Bob measures τ(y), what is the expectation value of σ(y)τ(y)?
