Classical Capacity of Single-Mode Bosonic Gaussian Channels
Abstract
The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number N and allowed average decoding error ε equals the vanishing-error capacity at mean photon number N/(1−ε). Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.
Related
- Efficient capacity-achieving entanglement generation with application to pure-loss Bosonic channels
- Energy-constrained two-way capacity bounds for noisy Gaussian channels
- The classical capacity of generalized amplitude-damping channels and its strong-converse exponent
- Feedback Capacity of Stationary Gaussian Channels: An Optimal Schalkwijk-Kailath Scheme
- When are bosonic Gaussian states classical to learn?
BibTeX
@misc{adesso2026classical,
title = {{Classical Capacity of Single-Mode Bosonic Gaussian Channels}},
author = {Gerardo Adesso and Ludovico Lami and Vittorio Giovannetti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22308},
eprint = {2610.22308},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22308},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical Capacity of Single-Mode Bosonic Gaussian Channels
AU - Gerardo Adesso
AU - Ludovico Lami
AU - Vittorio Giovannetti
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22308
UR - https://arxiv.org/abs/2610.22308
AB - The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number N and allowed average decoding error ε equals the vanishing-error capacity at mean photon number N/(1−ε). Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.
ER -