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For Kraus operators $A_j$, the Kraus formula for entanglement fidelity isIndeed each Kraus contribution to the purified-state overlap is $|⟨\Psi |(I\otimes A_j)|\Psi ⟩{|}^2$, and the expectation in a purification is $\mathrm{Tr}(\rho A_j)$. In this case,The entanglement fidelity of amplitude damping is thusFor $p=0$, this is one. For a ground-state input it is one for every $p$, whereas for an excited-state input it is $1-p$. These checks agree with the physical relaxation mechanism.