Teleportation-based collective attacks in Gaussian quantum key distribution

In Gaussian quantum key distribution eavesdropping attacks are conventionally modeled through the universal entangling cloner scheme, which is based on the premise that the whole environment is under control of the adversary, i.e., the eavesdropper purifies the system. This assumption implies that the eavesdropper has either access to an identity (noiseless) channel or an infinite amount of entanglement in order to simulate such an identity channel. In this work we challenge the necessity of this assumption and we propose a teleportation-based eavesdropping attack, where the eavesdropper is not assumed to have access to the shared channel, that represents the unavoidable noise due to the environment. Under collective measurements, this attack reaches optimality in the limit of an infinite amount of entanglement, while for finite entanglement resources it outperforms the corresponding optimal individual attack. We also calculate the minimum amount of distributed entanglement that is necessary for this eavesdropping scheme, since we consider it as the operationally critical quantity capturing the limitations of a realistic attack. We conclude that the fact that an infinite amount of entanglement is required for an optimal collective eavesdropping attack signifies the robustness of Gaussian quantum key distribution.