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A qubit is in the state
α
∣
0
⟩
+
β
∣
1
⟩
\alpha|0\rangle + \beta|1\rangle
α
∣0
⟩
+
β
∣1
⟩
with
∣
α
∣
2
+
∣
β
∣
2
=
1
|\alpha|^2 + |\beta|^2 = 1
∣
α
∣
2
+
∣
β
∣
2
=
1
. By the Born rule, the probability of measuring outcome 0 is:
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α
2
\alpha^2
α
2
∣
α
∣
2
|\alpha|^2
∣
α
∣
2
α
\alpha
α
∣
α
∣
|\alpha|
∣
α
∣
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