# Upper bounds on secret key agreement over lossy thermal bosonic channels

## TL;DR

This paper derives tighter upper bounds on the secret-key-agreement capacity of lossy thermal bosonic channels, improving the benchmarks for quantum repeater performance in realistic quantum communication scenarios.

## Contribution

It extends the teleportation simulation framework to the relative entropy of entanglement, leading to more accurate upper bounds for practical finite-size regimes.

## Key findings

- Tighter upper bounds on secret-key capacity for thermal bosonic channels.
- Implication that previous bounds were overly pessimistic for finite-size use.
- Facilitates easier identification of working quantum repeaters in practice.

## Abstract

Upper bounds on the secret-key-agreement capacity of a quantum channel serve as a way to assess the performance of practical quantum-key-distribution protocols conducted over that channel. In particular, if a protocol employs a quantum repeater, achieving secret-key rates exceeding these upper bounds is a witness to having a working quantum repeater. In this paper, we extend a recent advance [Liuzzo-Scorpo et al., arXiv:1705.03017] in the theory of the teleportation simulation of single-mode phase-insensitive Gaussian channels such that it now applies to the relative entropy of entanglement measure. As a consequence of this extension, we find tighter upper bounds on the non-asymptotic secret-key-agreement capacity of the lossy thermal bosonic channel than were previously known. The lossy thermal bosonic channel serves as a more realistic model of communication than the pure-loss bosonic channel, because it can model the effects of eavesdropper tampering and imperfect detectors. An implication of our result is that the previously known upper bounds on the secret-key-agreement capacity of the thermal channel are too pessimistic for the practical finite-size regime in which the channel is used a finite number of times, and so it should now be somewhat easier to witness a working quantum repeater when using secret-key-agreement capacity upper bounds as a benchmark.