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Multiple choice
Tracing out one qubit of
cos
(
π
/
6
)
∣
00
⟩
+
sin
(
π
/
6
)
∣
11
⟩
\cos(\pi/6)|00\rangle + \sin(\pi/6)|11\rangle
cos
(
π
/6
)
∣00
⟩
+
sin
(
π
/6
)
∣11
⟩
leaves
ρ
A
=
d
i
a
g
(
cos
2
(
π
/
6
)
,
sin
2
(
π
/
6
)
)
\rho_A = \mathrm{diag}(\cos^2(\pi/6), \sin^2(\pi/6))
ρ
A
=
diag
(
cos
2
(
π
/6
)
,
sin
2
(
π
/6
))
. The purity is
T
r
(
ρ
A
2
)
=
cos
4
(
π
/
6
)
+
sin
4
(
π
/
6
)
\mathrm{Tr}(\rho_A^2) = \cos^4(\pi/6) + \sin^4(\pi/6)
Tr
(
ρ
A
2
)
=
cos
4
(
π
/6
)
+
sin
4
(
π
/6
)
. What is it?
🔬 try it before you answer
1.0 (forgot the state is mixed)
0.75 (used
cos
2
\cos^2
cos
2
only)
0.5 (assumed maximally mixed)
0.625
Check answer