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Multiple choice
For
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
]
, the Bloch vector is
r
x
=
2
R
e
(
ρ
01
)
r_x = 2\,\mathrm{Re}(\rho_{01})
r
x
=
2
Re
(
ρ
01
)
,
r
y
=
−
2
I
m
(
ρ
01
)
r_y = -2\,\mathrm{Im}(\rho_{01})
r
y
=
−
2
Im
(
ρ
01
)
,
r
z
=
ρ
00
−
ρ
11
r_z = \rho_{00} - \rho_{11}
r
z
=
ρ
00
−
ρ
11
. What is the length
∣
r
∣
=
r
x
2
+
r
y
2
+
r
z
2
|r| = \sqrt{r_x^2 + r_y^2 + r_z^2}
∣
r
∣
=
r
x
2
+
r
y
2
+
r
z
2
?
🔬 try it before you answer
1
/
2
≈
0.7071
1/\sqrt{2} \approx 0.7071
1/
2
≈
0.7071
0.5 (used
r
z
r_z
r
z
only)
1.0 (assumed a pure state)
0.559 (forgot the factor of 2 on
r
x
r_x
r
x
)
Check answer