Theory of channel simulation and bounds for private communication

We review recent results on the simulation of quantum channels, the reduction of adaptive protocols (teleportation stretching), and the derivation of converse boundsfor quantum and private communication, as established in PLOB(Pirandola et al 2017Nat. Commun. 8 15043).We start by introducing a general weak converse boundfor private communication based on the relative entropy of entanglement. We discuss how combining this bound with channel simulation and teleportation stretching, PLOB established the two-way quantum and private capacities of severalfundamental channels, including the bosonic lossy channel.We then provide a rigorous proof of the strong converse property of these bounds by adopting a correct use of the Braunstein–Kimble teleportation protocolfor the simulation of bosonic Gaussian channels. This analysis provides afull justification of claims presented in thefollow-up paper WTB(Wilde et al 2017 IEEE Trans. Inf. Theory 63 1792–817)whose upper boundsfor Gaussian channels would be otherwise infinitely large. Besides clarifying contributions in the area of channel simulation and protocol reduction, we also present some generalizations of the tools to other entanglement measures and novel results on the maximum excess noise which is tolerable in quantum key distribution.