Finite-resource teleportation stretching for continuous-variable systems

We show how adaptive protocols of quantum and private communication through bosonic Gaussian channels can be simplified into much easier block versions that involve resource states with finite energy. This is achieved by combining the adaptive-to-block reduction technique devised in [Pirandola et al., arXiv:1510.08863], based on teleportation stretching and relative entropy of entanglement, with the simulation of Gaussian channels introduced by [Liuzzo-Scorpo et al., arXiv:1705.03017]. In this way, we derive weak converse upper bounds for the secret-key capacity of phase-insensitive Gaussian channels, which closely approximate the optimal limit for infinite energy. Our results apply to both point-to-point and repeater-assisted private communications.