Equivalence between Entanglement and the Optimal Fidelity of Continuous Variable Teleportation

Abstract

We devise the optimal form of Gaussian resource states enabling continuous variable teleportation with maximal fidelity. We show that a nonclassical optimal fidelity of $N$-user teleportation networks is {\it necessary and sufficient} for $N$-party entangled Gaussian resources, yielding an estimator of multipartite entanglement. This {\it entanglement of teleportation} is equivalent to entanglement of formation in the two-user protocol, and to localizable entanglement in the multi-user one. The continuous-variable tangle, quantifying entanglement sharing in three-mode Gaussian states, is operationally linked to the optimal fidelity of a tripartite teleportation network.