|q⟩
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A bit-flip channel
E
(
ρ
)
=
(
1
−
p
)
ρ
+
p
X
ρ
X
E(\rho) = (1-p)\rho + p X \rho X
E
(
ρ
)
=
(
1
−
p
)
ρ
+
pX
ρX
with
p
=
0.25
p = 0.25
p
=
0.25
acts on
ρ
=
∣
+
⟩
⟨
+
∣
=
[
0.5
0.5
0.5
0.5
]
\rho = |+\rangle\langle+| = \begin{bmatrix}0.5 & 0.5 \\ 0.5 & 0.5\end{bmatrix}
ρ
=
∣
+
⟩
⟨
+
∣
=
[
0.5
0.5
0.5
0.5
]
, where
X
X
X
is the Pauli-X gate. What is
⟨
0
∣
E
(
ρ
)
∣
0
⟩
\langle 0|E(\rho)|0\rangle
⟨
0∣
E
(
ρ
)
∣0
⟩
?
🔬 try it before you answer
0.375
0.75
0.5
0.25
Check answer