# Optimal continuous-variable teleportation under energy constraint

## TL;DR

This paper investigates the maximum achievable fidelity in continuous-variable quantum teleportation under energy constraints, identifying optimal quantum states and demonstrating that non-Gaussian states offer slight improvements over Gaussian states.

## Contribution

It introduces a formalism to evaluate teleportation fidelity and proves that non-Gaussian photon-number entangled states are rigorously optimal under energy constraints.

## Key findings

- Optimal states are photon-number entangled states.
- Gaussian states are near-optimal.
- Non-Gaussian states provide slight fidelity improvements.

## Abstract

Quantum teleportation is one of the crucial protocols in quantum information processing. It is important to accomplish an efficient teleportation under practical conditions, aiming at a higher fidelity desirably using fewer resources. The continuous-variable (CV) version of quantum teleportation was first proposed using a Gaussian state as a quantum resource, while other attempts were also made to improve performance by applying non-Gaussian operations. We investigate the CV teleportation to find its ultimate fidelity under energy constraint identifying an optimal quantum state. For this purpose, we present a formalism to evaluate teleportation fidelity as an expectation value of an operator. Using this formalism, we prove that the optimal state must be a form of photon-number entangled states. We further show that Gaussian states are near-optimal while non-Gaussian states make a slight improvement and therefore are rigorously optimal, particularly in the low-energy regime.