= Entanglement fidelity of amplitude damping
{title2=$F_e=\tfrac14[1+s_z+\sqrt{1-p}(1-s_z)]^2+\tfrac p4(s_x^2+s_y^2)$}
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 $1-p$.
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