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Gaussian Optimality of Energy-Constrained One-Shot Communication through Single-Mode Bosonic Gaussian Channels — arXiv:2608.17239

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.17239
License (as archived): CC0-1.0
Archived: 2026-10-18T15:45:54.472Z
SHA-256 of the archived text: 956091a16d8453f6c11e5dbf3e648f2f73e743175e03ff1e85140257202c19c2
Stable URL of this page: https://metraipolis.com/documento/dc_bb2d348fb94d

How to cite

Gaussian Optimality of Energy-Constrained One-Shot Communication through Single-Mode Bosonic Gaussian Channels — arXiv:2608.17239 — arXiv (en), https://arxiv.org/abs/2608.17239 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bb2d348fb94d (Metraipolis archive dc_bb2d348fb94d, sha256 956091a16d8453f6c11e5dbf3e648f2f73e743175e03ff1e85140257202c19c2)

BibTeX

@misc{dcbb2d348fb94d,
  title = {Gaussian Optimality of Energy-Constrained One-Shot Communication through Single-Mode Bosonic Gaussian Channels — arXiv:2608.17239},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.17239},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bb2d348fb94d; sha256 956091a16d8453f6c11e5dbf3e648f2f73e743175e03ff1e85140257202c19c2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.17239. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-08-19 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2608.17239 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T15:39:32.432Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-08-19?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).