Gaussian Optimality of Energy-Constrained One-Shot Communication through Single-Mode Bosonic Gaussian Channels
Abstract
We prove Gaussian optimality for the energy-constrained one-shot Holevo capacity of single-mode bosonic Gaussian channels, including phase-sensitive channels with arbitrarily squeezed thermal noise. The unresolved regime is the low energy branch, where the Gaussian optimizer modulates only one quadrature and minimum-output-entropy arguments cannot decouple the average state from the letters. For pure one-mode dilations we retain a stronger pointwise result: moment-matched Gaussianization improves the fixed average Holevo function for every input. For mixed environments, whose purification produces a 1:2 entanglement-of-formation problem, we avoid any generic 1:2 Gaussian extremality conjecture. The optimal Gaussian letter selects an effective environmental Schmidt mode and an affine two-mode EPR witness. Its null direction is exactly the modulated quadrature, while its slope equals the negative derivative of the Gaussian letter-output entropy. This produces a supporting lower bound on the dilated entanglement of formation; Gaussian maximum entropy and concavity then give a global upper bound tangent at the Gaussian optimizer. Consequently the known Gaussian formulas for attenuating, amplifying, phase-conjugating, and additive-noise fiducial channels are exact over unrestricted ensembles at every input energy. Via the passive-input fiducial decomposition and energy-constrained continuity, the result extends to every single-mode Gaussian channel, including lower-rank canonical limits. No additivity across channel uses is assumed.
Related
- Energy-constrained two-way capacity bounds for noisy Gaussian channels
- Optimality of Gaussian Entanglement of Formation
- The exact strong converse exponent for private communication over quantum channels
- Private communication from Pauli channels with no privacy
- Thermodynamic efficiency of communication channels
BibTeX
@misc{ji2026gaussian,
title = {{Gaussian Optimality of Energy-Constrained One-Shot Communication through Single-Mode Bosonic Gaussian Channels}},
author = {Se-Wan Ji},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.17239},
eprint = {2608.17239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17239},
}
RIS
TY - UNPB
TI - Gaussian Optimality of Energy-Constrained One-Shot Communication through Single-Mode Bosonic Gaussian Channels
AU - Se-Wan Ji
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2608.17239
UR - https://arxiv.org/abs/2608.17239
AB - We prove Gaussian optimality for the energy-constrained one-shot Holevo capacity of single-mode bosonic Gaussian channels, including phase-sensitive channels with arbitrarily squeezed thermal noise. The unresolved regime is the low energy branch, where the Gaussian optimizer modulates only one quadrature and minimum-output-entropy arguments cannot decouple the average state from the letters. For pure one-mode dilations we retain a stronger pointwise result: moment-matched Gaussianization improves the fixed average Holevo function for every input. For mixed environments, whose purification produces a 1:2 entanglement-of-formation problem, we avoid any generic 1:2 Gaussian extremality conjecture. The optimal Gaussian letter selects an effective environmental Schmidt mode and an affine two-mode EPR witness. Its null direction is exactly the modulated quadrature, while its slope equals the negative derivative of the Gaussian letter-output entropy. This produces a supporting lower bound on the dilated entanglement of formation; Gaussian maximum entropy and concavity then give a global upper bound tangent at the Gaussian optimizer. Consequently the known Gaussian formulas for attenuating, amplifying, phase-conjugating, and additive-noise fiducial channels are exact over unrestricted ensembles at every input energy. Via the passive-input fiducial decomposition and energy-constrained continuity, the result extends to every single-mode Gaussian channel, including lower-rank canonical limits. No additivity across channel uses is assumed.
ER -