Theory of channel simulation and bounds for private communication

TL;DR

This paper reviews recent advances in quantum channel simulation, teleportation stretching, and bounds for private communication, establishing fundamental capacities and properties of quantum channels with rigorous proofs.

Contribution

It provides a rigorous proof of the strong converse property for quantum channel bounds and extends tools to other entanglement measures and quantum key distribution.

Findings

Established two-way quantum and private capacities for key channels

Provided a rigorous proof of the strong converse property for Gaussian channels

Presented bounds on maximum excess noise in quantum key distribution

Abstract

We review recent results on the simulation of quantum channels, the reduction of adaptive protocols (teleportation stretching), and the derivation of converse bounds for quantum and private communication, as established in PLOB [Pirandola, Laurenza, Ottaviani, Banchi, arXiv:1510.08863]. We start by introducing a general weak converse bound for 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 several fundamental 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 protocol for the simulation of bosonic Gaussian channels. This analysis provides a full justification of claims presented in the follow-up paper WTB [Wilde, Tomamichel, Berta, arXiv:1602.08898] whose upper bounds for 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.