Energy-constrained two-way capacity bounds for noisy Gaussian channels
Abstract
A gap between achievable rates and converse bounds persists for energy-constrained bosonic communication in the presence of excess noise. We derive a unified adaptive weak-converse bound for thermal attenuation, noisy amplification, and additive Gaussian noise under an unconditional mean transmitted-photon-number constraint. The bound applies to arbitrary adaptive protocols with quantum memories and constrains the two-way quantum, entanglement-distribution, private, and secret-key capacities. It vanishes throughout the entanglement-breaking region and approaches the corresponding PLOB bound at infinite energy. At finite energy, it improves the evaluated Gaussian squashed-entanglement and PLOB bounds in relevant parameter regimes, while comparison with hashing rates quantifies the remaining gap to achievability. The result provides a common energy-dependent benchmark for noisy bosonic Gaussian channels and extends finite-energy converse methods beyond the quantum-limited setting.
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BibTeX
@misc{pirandola2026energyconstrained,
title = {{Energy-constrained two-way capacity bounds for noisy Gaussian channels}},
author = {Stefano Pirandola},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08786},
eprint = {2610.08786},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08786},
}
RIS
TY - UNPB
TI - Energy-constrained two-way capacity bounds for noisy Gaussian channels
AU - Stefano Pirandola
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.08786
UR - https://arxiv.org/abs/2610.08786
AB - A gap between achievable rates and converse bounds persists for energy-constrained bosonic communication in the presence of excess noise. We derive a unified adaptive weak-converse bound for thermal attenuation, noisy amplification, and additive Gaussian noise under an unconditional mean transmitted-photon-number constraint. The bound applies to arbitrary adaptive protocols with quantum memories and constrains the two-way quantum, entanglement-distribution, private, and secret-key capacities. It vanishes throughout the entanglement-breaking region and approaches the corresponding PLOB bound at infinite energy. At finite energy, it improves the evaluated Gaussian squashed-entanglement and PLOB bounds in relevant parameter regimes, while comparison with hashing rates quantifies the remaining gap to achievability. The result provides a common energy-dependent benchmark for noisy bosonic Gaussian channels and extends finite-energy converse methods beyond the quantum-limited setting.
ER -