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Multiple choice
For
∣
ψ
⟩
=
cos
(
θ
)
∣
0
⟩
+
sin
(
θ
)
∣
1
⟩
|\psi\rangle = \cos(\theta)|0\rangle + \sin(\theta)|1\rangle
∣
ψ
⟩
=
cos
(
θ
)
∣0
⟩
+
sin
(
θ
)
∣1
⟩
with
θ
=
π
/
6
\theta = \pi/6
θ
=
π
/6
, and
∣
+
⟩
=
(
∣
0
⟩
+
∣
1
⟩
)
/
2
|+\rangle = (|0\rangle + |1\rangle)/\sqrt{2}
∣
+
⟩
=
(
∣0
⟩
+
∣1
⟩)
/
2
, what is
p
(
+
)
=
∣
⟨
+
∣
ψ
⟩
∣
2
=
(
1
/
2
)
(
cos
(
θ
)
+
sin
(
θ
)
)
2
p(+) = |\langle+|\psi\rangle|^2 = (1/2)(\cos(\theta) + \sin(\theta))^2
p
(
+
)
=
∣
⟨
+
∣
ψ
⟩
∣
2
=
(
1/2
)
(
cos
(
θ
)
+
sin
(
θ
)
)
2
?
≈ 0.067 (using
cos
−
sin
\cos - \sin
cos
−
sin
)
0.5
≈ 1.366 (forgetting the 1/2 factor)
≈ 0.933
Check answer