Channel fidelities for high-fidelity approach in KLM scheme

We study channel fidelity for the high-fidelity approach in the Knill-Laflamme-Milburn (KLM) scheme. We examine an optimal channel fidelity $f_{opt}$ and identify the corresponding KLM ancilla state. In the limit of large $n$, where $2n$ is the number of the ancilla qubits, we find $f_{opt}=1-\frac{{\pi }^2}{6n^2}+\frac{2{\pi }^2}{9n^3}$. We see that as $n$ increases $f_{opt}$ approaches to 1 slightly faster than $f=1-\frac{2}{n^2}$ which is the channel fidelity computed by Franson et. al. in the limit of large $n$. We also compute the channel fidelity for the ancilla state that gives a lower bound of success probability of quantum teleportation.