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The two-way capacities of quantum channels determine the ultimateentanglement and secret-key distribution rates achievable by two distantparties that are connected by a noisy transmission line, in absence of quantumrepeaters. Since repeaters will likely be expensive to build and maintain, acentral open problem of quantum communication is to understand whatperformances are achievable without them. In this paper, we find a new lowerbound on the energy-constrained and unconstrained two-way quantum andsecret-key capacities of all phase-insensitive bosonic Gaussian channels,namely thermal attenuator, thermal amplifier, and additive Gaussian noise,which are realistic models for the noise affecting optical fibres or free-spacelinks. Ours is the first nonzero lower bound on the two-way quantum capacity inthe parameter range where the (reverse) coherent information becomes negative,and it shows explicitly that entanglement distribution is always possible whenthe channel is not entanglement breaking. This completely solves a crucial openproblem of the field, namely, establishing the maximum excess noise which istolerable in continuous-variable quantum key distribution. In addition, ourconstruction is fully explicit, i.e. we devise and optimise a concreteentanglement distribution and distillation protocol that works by combiningrecurrence and hashing protocols

Maximum tolerable excess noise in CV-QKD and improved lower bound on two-way capacities