Channel fidelities for high-fidelity approach in KLM scheme

TL;DR

This paper analyzes the channel fidelity in the high-fidelity approach of the KLM quantum teleportation scheme, deriving optimal fidelity expressions and comparing them with previous results.

Contribution

It identifies the optimal ancilla state for high-fidelity quantum teleportation in the KLM scheme and derives an explicit formula for the channel fidelity as the number of ancilla qubits grows.

Findings

Optimal channel fidelity approaches 1 faster than previous estimates as n increases.

Derived explicit formula for $f_{opt}$ in the large n limit.

Compared channel fidelity for optimal and lower-bound ancilla states.

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.