Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation

TL;DR

This paper analytically determines the optimal input states for assessing the performance of continuous-variable quantum teleportation, showing that finite entangled superpositions of twin-Fock states are optimal under energy constraints.

Contribution

It introduces an analytical method to identify unique optimal input states for continuous-variable teleportation performance evaluation under energy constraints.

Findings

Optimal states are finite entangled superpositions of twin-Fock states.

These states are proven to be unique under the given energy constraints.

The approach quantifies performance via energy-constrained channel fidelity.

Abstract

Continuous-variable (CV) teleportation is a foundational protocol in quantum information science. A number of experiments have been designed to simulate ideal teleportation under realistic conditions. In this paper, we detail an analytical approach for determining optimal input states for quantifying the performance of CV unidirectional and bidirectional teleportation. The metric that we consider for quantifying performance is the energy-constrained channel fidelity between ideal teleportation and its experimental implementation, and along with this, our focus is on determining optimal input states for distinguishing the ideal process from the experimental one. We prove that, under certain energy constraints, the optimal input state in unidirectional, as well as bidirectional, teleportation is a finite entangled superposition of twin-Fock states saturating the energy constraint. Moreover, we also prove that, under the same constraints, the optimal states are unique; that is, there is no other optimal finite entangled superposition of twin-Fock states.