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Lower bounding the secret key capacity of bosonic Gaussian channels via optimal Gaussian measurements

Giuseppe Ortolano1,2, Stefano Pirandola3, and Leonardo Banchi1,2

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Phys. Rev. A 114, 042464 – Published 28 October, 2026

DOI: https://doi.org/10.1103/v53z-9gtm

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.

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Phys. Rev. A 114, 042464– Published 28 October, 2026
  • Received 12 February 2026
  • Revised 8 June 2026
  • Accepted 2 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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