Teleportation simulation of bosonic Gaussian channels: Strong and uniform convergence
arXiv:1712.01615 · doi:10.1140/epjd/e2018-90253-1
Abstract
We consider the Braunstein-Kimble protocol for continuous variable teleportation and its application for the simulation of bosonic channels. We discuss the convergence properties of this protocol under various topologies (strong, uniform, and bounded-uniform) clarifying some typical misinterpretations in the literature. We then show that the teleportation simulation of an arbitrary single-mode Gaussian channel is uniformly convergent to the channel if and only if its noise matrix has full rank. The various forms of convergence are then discussed within adaptive protocols, where the simulation error must be propagated to the output of the protocol by means of a "peeling" argument, following techniques from PLOB [arXiv:1510.08863]. Finally, as an application of the peeling argument and the various topologies of convergence, we provide complete rigorous proofs for recently-claimed strong converse bounds for private communication over Gaussian channels.
Accepted version. Establishes a general criterion for the uniform convergence of teleportation simulation for an arbitrary Gaussian channel. Clarifying the use of the Braunstein-Kimble teleportation protocol, it also provides complete proofs for the claims presented in WTB arXiv:1602.08898, beyond the first rigorous proof already given in arXiv:1711.09909
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