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An amplitude-damping channel with damping probability
g
=
0.3
g = 0.3
g
=
0.3
has Kraus operators
K
0
=
[
1
0
0
1
−
g
]
K_0 = \begin{bmatrix}1 & 0 \\ 0 & \sqrt{1-g}\end{bmatrix}
K
0
=
[
1
0
0
1
−
g
]
and
K
1
=
[
0
g
0
0
]
K_1 = \begin{bmatrix}0 & \sqrt{g} \\ 0 & 0\end{bmatrix}
K
1
=
[
0
0
g
0
]
. It acts on
ρ
=
∣
1
⟩
⟨
1
∣
\rho = |1\rangle\langle 1|
ρ
=
∣1
⟩
⟨
1∣
. What is the resulting excited-state population
⟨
1
∣
E
(
ρ
)
∣
1
⟩
\langle 1|E(\rho)|1\rangle
⟨
1∣
E
(
ρ
)
∣1
⟩
?
🔬 try it before you answer
0.3
0.49
0.84
0.7
Check answer