Entanglement fidelity of amplitude damping ($F_e=\frac{1}{4}[1+s_z+\sqrt{1-p}(1-s_z){]}^2+\frac{p}{4}(s_x^2+s_y^2)$)

The Kraus formula for entanglement fidelity applies to any input, including mixed qubit states. For the amplitude damping channel, the diagonal Kraus trace is $[1+s_z+\sqrt{1-p}(1-s_z)]/2$ and the jump Kraus trace has squared modulus $p(s_x^2+s_y^2)/4$. Summing them gives the formula. Ground-state inputs have unit entanglement fidelity; excited-state inputs have fidelity $1-p$.