|q⟩
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For the state
∣
ψ
⟩
=
(
∣
0
⟩
+
∣
1
⟩
)
/
2
|\psi\rangle = (|0\rangle + |1\rangle)/\sqrt{2}
∣
ψ
⟩
=
(
∣0
⟩
+
∣1
⟩)
/
2
, the Hermitian operator
Z
Z
Z
(Pauli-Z) has eigenvalues
+
1
+1
+
1
on
∣
0
⟩
|0\rangle
∣0
⟩
and
−
1
-1
−
1
on
∣
1
⟩
|1\rangle
∣1
⟩
. What is
⟨
Z
⟩
=
∣
α
∣
2
⋅
(
+
1
)
+
∣
β
∣
2
⋅
(
−
1
)
\langle Z\rangle = |\alpha|^2 \cdot (+1) + |\beta|^2 \cdot (-1)
⟨
Z
⟩
=
∣
α
∣
2
⋅
(
+
1
)
+
∣
β
∣
2
⋅
(
−
1
)
, with
∣
α
∣
2
=
∣
β
∣
2
=
1
/
2
|\alpha|^2 = |\beta|^2 = 1/2
∣
α
∣
2
=
∣
β
∣
2
=
1/2
?
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1/2
-1
1
0
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