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A noisy magic state is the depolarizing mixture
ρ
=
(
1
−
p
)
∣
T
⟩
⟨
T
∣
+
p
(
I
/
2
)
\rho = (1 - p)|T\rangle\langle T| + p(I/2)
ρ
=
(
1
−
p
)
∣
T
⟩
⟨
T
∣
+
p
(
I
/2
)
. Its infidelity to the ideal
∣
T
⟩
|T\rangle
∣
T
⟩
is
1
−
⟨
T
∣
ρ
∣
T
⟩
1 - \langle T|\rho|T\rangle
1
−
⟨
T
∣
ρ
∣
T
⟩
, where
⟨
T
∣
(
I
/
2
)
∣
T
⟩
=
1
/
2
\langle T|(I/2)|T\rangle = 1/2
⟨
T
∣
(
I
/2
)
∣
T
⟩
=
1/2
. For
p
=
0.08
p = 0.08
p
=
0.08
, what is the input error
1
−
⟨
T
∣
ρ
∣
T
⟩
1 - \langle T|\rho|T\rangle
1
−
⟨
T
∣
ρ
∣
T
⟩
?
0.04
0.16
0.92
0.08
Check answer