|q⟩
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For the state
∣
ψ
⟩
=
(
∣
0
⟩
+
∣
1
⟩
)
/
2
|\psi\rangle = (|0\rangle + |1\rangle)/\sqrt{2}
∣
ψ
⟩
=
(
∣0
⟩
+
∣1
⟩)
/
2
, what is the expectation value
⟨
σ
z
⟩
=
⟨
ψ
∣
σ
z
∣
ψ
⟩
\langle\sigma_z\rangle = \langle\psi|\sigma_z|\psi\rangle
⟨
σ
z
⟩
=
⟨
ψ
∣
σ
z
∣
ψ
⟩
, where
σ
z
\sigma_z
σ
z
acts as
+
1
+1
+
1
on
∣
0
⟩
|0\rangle
∣0
⟩
and
−
1
-1
−
1
on
∣
1
⟩
|1\rangle
∣1
⟩
?
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1
0
1/2
-1
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