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Multiple choice
A qubit has density matrix
ρ
=
[
0.75
0.25
0.25
0.25
]
\rho = \begin{bmatrix}0.75 & 0.25 \\ 0.25 & 0.25\end{bmatrix}
ρ
=
[
0.75
0.25
0.25
0.25
]
. With
Z
=
[
1
0
0
−
1
]
Z = \begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}
Z
=
[
1
0
0
−
1
]
, the expectation value is
⟨
Z
⟩
=
T
r
(
ρ
Z
)
\langle Z\rangle = \mathrm{Tr}(\rho Z)
⟨
Z
⟩
=
Tr
(
ρZ
)
. What is
⟨
Z
⟩
\langle Z\rangle
⟨
Z
⟩
?
🔬 try it before you answer
-0.5 (sign flip)
1.0 (took the trace of
ρ
\rho
ρ
instead)
0.5
0.25 (used the off-diagonal element)
Check answer