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With Pauli matrices
X
=
[
0
1
1
0
]
X = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}
X
=
[
0
1
1
0
]
and
Z
=
[
1
0
0
−
1
]
Z = \begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}
Z
=
[
1
0
0
−
1
]
, compute the commutator
[
X
,
Z
]
=
X
Z
−
Z
X
[X,Z] = XZ - ZX
[
X
,
Z
]
=
X
Z
−
Z
X
. What is its (0,1) entry?
-2
-1
2
0 (
X
X
X
and
Z
Z
Z
commute)
Check answer