Necessary and Sufficient Criteria for Gaussian Quantum Teleportation

TL;DR

This paper proves that for Gaussian entangled states, EPR correlation is sufficient for quantum teleportation, and for some states, it is both necessary and sufficient, offering a complete resource characterization.

Contribution

It provides an analytic proof that EPR correlation is sufficient for Gaussian quantum teleportation and identifies conditions under which it is also necessary.

Findings

EPR correlation is sufficient for Gaussian QT.

For certain Gaussian states, EPR correlation is necessary and sufficient.

The results offer a complete characterization of resources for QT.

Abstract

Quantum teleportation (QT) serves as one of the building blocks of the current state information science and technology which necessitates proper characterization of the resources yielding QT. While entanglement is known to be the basic requirement to achieve QT, condition of sufficiency for QT still remains an open question. Here, we provide an analytic proof that in the case of Gaussian entangled resources, in general, Einstein-Podolsky-Rosen (EPR) correlation is {\em sufficient for QT}. For a relatively restricted set of Gaussian states we provide even a tighter condition that EPR correlation is {\em both necessary and sufficient for QT}. Our results, in turn, provide a complete characterization of the resources required for QT.