Lower Bounding the Secret Key Capacity of Bosonic Gaussian Channels via Optimal Gaussian Measurements

TL;DR

This paper derives a lower bound on the secret key capacity of bosonic Gaussian channels using optimal Gaussian measurements, confirming the optimality of certain protocols and improving bounds for specific channels.

Contribution

It introduces a method to lower bound secret key capacity with optimal Gaussian measurements, simplifying evaluation and improving bounds for some channels.

Findings

Optimality of previous protocols for thermal-loss and thermal amplification channels.

Simplified formulas for performance evaluation of these channels.

Improved lower bounds for the added noise channel.

Abstract

We find the maximum rate achievable in the private communication over a bosonic quantum channel with a fully Gaussian protocol based on optimal single-mode Gaussian measurements. This rate establishes a lower bound on the secret rate capacity of the channel. We focus on the class of phase-insensitive Gaussian channels. For the thermal-loss and thermal amplification channels, our results demonstrate the optimality, within the constraints of our analysis, of previously proposed protocols, while also providing a significantly simplified formula for their performance evaluation. For the added noise channel, our rate provides a better lower bound than any previously known.