Regularized classical capacity and additivity for single-mode bosonic Gaussian channels

Determine the regularized classical capacity of a single-mode bosonic Gaussian channel under an average photon-number constraint, or equivalently establish additivity of the one-shot Holevo capacity through an appropriate multimode formation witness or strong-superadditivity principle.

Background

The paper proves Gaussian optimality for the one-shot Holevo capacity of every single-mode bosonic Gaussian channel, including phase-sensitive channels with squeezed thermal noise. It does not extend this result to correlated inputs across multiple channel uses. For multiple uses, the relevant entanglement-of-formation term involves arbitrary multimode bipartitions, while the single-use tangent EPR witness controls only the one-mode structure.

Resolving the regularized capacity would require a genuinely multimode result, such as a global formation witness or a strong-superadditivity theorem. Establishing additivity would identify the asymptotic classical capacity with the one-shot Gaussian formula proved in the paper.

References

Consequently the regularized classical capacity C(\Phi,\bar N)=\lim_{n\to\infty}\frac1n C_\chi{(1)}(\Phi{\otimes n},n\bar N) is not determined here. Proving additivity would require an additional multimode statement, such as a suitable global formation witness or a strong-superadditivity principle.

— Gaussian Optimality of Energy-Constrained One-Shot Communication through Single-Mode Bosonic Gaussian Channels  (2608.17239 - Ji, 18 Aug 2026) in Section “Why the result remains one-shot”