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Using the Pauli operator
σ
x
=
[
0
1
1
0
]
\sigma_x = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}
σ
x
=
[
0
1
1
0
]
and the column vector
∣
+
x
⟩
=
(
1
/
2
)
[
1
1
]
|{+x}\rangle = (1/\sqrt{2})\begin{bmatrix}1 \\ 1\end{bmatrix}
∣
+
x
⟩
=
(
1/
2
)
[
1
1
]
, compute the expectation value
⟨
+
x
∣
σ
x
∣
+
x
⟩
\langle{+x}|\sigma_x|{+x}\rangle
⟨
+
x
∣
σ
x
∣
+
x
⟩
. What is its value?
🔬 try it before you answer
1
0
-1
1
/
2
≈
0.707
1/\sqrt{2} \approx 0.707
1/
2
≈
0.707
Check answer