|q⟩
Bad Qubits
Play
Quest
Questions
Learn
Playground
☕
← Question Bank
Multiple choice
Two qubits are in the state
cos
(
π
/
8
)
∣
00
⟩
+
sin
(
π
/
8
)
∣
11
⟩
\cos(\pi/8)|00\rangle + \sin(\pi/8)|11\rangle
cos
(
π
/8
)
∣00
⟩
+
sin
(
π
/8
)
∣11
⟩
. Tracing out qubit B gives the diagonal reduced density matrix
ρ
A
=
d
i
a
g
(
cos
2
(
π
/
8
)
,
sin
2
(
π
/
8
)
)
\rho_A = \mathrm{diag}(\cos^2(\pi/8), \sin^2(\pi/8))
ρ
A
=
diag
(
cos
2
(
π
/8
)
,
sin
2
(
π
/8
))
. Compute purity
T
r
(
ρ
A
2
)
\mathrm{Tr}(\rho_A^2)
Tr
(
ρ
A
2
)
PLUS
⟨
Z
⟩
=
T
r
(
ρ
A
Z
)
\langle Z\rangle = \mathrm{Tr}(\rho_A Z)
⟨
Z
⟩
=
Tr
(
ρ
A
Z
)
, where
Z
=
d
i
a
g
(
1
,
−
1
)
Z = \mathrm{diag}(1, -1)
Z
=
diag
(
1
,
−
1
)
. What is the sum?
🔬 try it before you answer
≈ 0.8536 (purity
T
r
(
ρ
A
2
)
\mathrm{Tr}(\rho_A^2)
Tr
(
ρ
A
2
)
only)
≈ 0.7071 (
⟨
Z
⟩
\langle Z\rangle
⟨
Z
⟩
only)
≈ 1.7071 (used
⟨
Z
⟩
=
cos
2
+
sin
2
=
1
\langle Z\rangle = \cos^2 + \sin^2 = 1
⟨
Z
⟩
=
cos
2
+
sin
2
=
1
)
≈ 1.4571
Check answer