Channel fidelities for high-fidelity approach in KLM scheme

Abstract

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-{\pi^{2} \over 6n^{2}}+{2\pi^{2} \over 9n^{3}}. We see that as n increases f_{opt} approaches to 1 slightly faster than f=1-{2 \over 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.