Lower Bounds of Success Probabilities for High-Fidelity Approach in KLM Scheme

In the Knill-Laflamme-Milburn (KLM) scheme, the success probability of quantum teleportation is given by $\frac{n}{n+1}$, wehre $2n$ is the number of the ancilla qubits. For the high-fidelity approach in the KLM scheme, the success probability is approximately given by $1-\frac{1}{n^2}$ for large $n$. We give an explicit prescription to prepare an optimal ancilla state and give an exact lower bound of the success probability for the high-fidelity approach for arbitrary $n$.