Non-Gaussian communication beyond the thermal threshold

The problem asks whether thermal inputs optimize coherent information among Gaussian inputs to a bosonic thermal attenuator, and whether non-Gaussian inputs can extend the positive-capacity region. The 2026 paper answers both questions affirmatively.

Known results

• Holevo and Werner, 1999: the thermal-state coherent-information expression was the standard lower bound for the channel’s quantum capacity.

2026 non-Gaussian improvement

• For every $0<\nu$ and $0<\nu<1$? The paper proves, for the relevant attenuator parameters, that the supremum over single-mode Gaussian inputs is attained by thermal states in the infinite-energy limit, with value $\left[\log_{2}\frac{\eta}{1-\eta}-g(\nu)\right]_{+}$.
• At $\nu=1$ and $\eta=4/5$, all Gaussian inputs have coherent information $0$, while an explicit rank-two state supported on six Fock levels achieves at least $4.7\times10^{-4}$ qubits per use; hence $Q(\Phi_{4/5,1})>0$.
• Positive coherent information is rigorously certified down to $\eta=0.7841$, while antidegradability forces zero capacity for $\eta\leq3/4$; the reported value at $\eta=0.7818$ remains numerical only.

Current status (as of July 2026): The Gaussian optimization and existence of a non-Gaussian improvement are settled, but the exact positive-capacity threshold remains open, with $3/4\leq\eta_c\leq0.7841$ established for $\nu=1$.