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For the 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
]
, the commutator is
[
X
,
Z
]
=
X
Z
−
Z
X
[X,Z] = XZ - ZX
[
X
,
Z
]
=
X
Z
−
Z
X
. What is the value of the bottom-left (row 2, column 1) entry of
[
X
,
Z
]
[X,Z]
[
X
,
Z
]
, divided by 2?
🔬 try it before you answer
1
-1
i
i
i
2
Check answer