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The amplitude-damping channel with
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
]
. Compute the completeness sum
M
=
K
0
†
K
0
+
K
1
†
K
1
M = K_0^\dagger K_0 + K_1^\dagger K_1
M
=
K
0
†
K
0
+
K
1
†
K
1
and report the Frobenius distance to the identity,
∑
i
j
(
M
i
j
−
I
i
j
)
2
\sqrt{\sum_{ij} (M_{ij} - I_{ij})^2}
∑
ij
(
M
ij
−
I
ij
)
2
. What is this value?
🔬 try it before you answer
0.55
0.42
0
0.3
Check answer