发表机构
The Affiliated Institute of ETRI（韩国电子通信研究院附属研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了带任意压缩热噪声的单模玻色高斯信道的能量受限单次Holevo容量具有高斯最优性，其结果可扩展至各类单模高斯信道，无需假设信道使用间的加性。
AI 中文摘要
我们证明了能量受限的单模玻色高斯信道的单次Holevo容量具有高斯最优性，包括带有任意压缩热噪声的相敏信道。未解决的区域是低能分支，其中高斯优化器仅调制一个正交分量，且最小输出熵论证无法将平均态与字母解耦。对于纯单模膨胀，我们保留了更强的逐点结果：矩匹配高斯化对每个输入都改善了固定平均Holevo函数。对于混合环境，其纯化产生1:2的形成纠缠问题，我们避免了任何通用的1:2高斯极值猜想。最优高斯字母选择了一个有效的环境Schmidt模和一个仿射双模EPR见证。其零方向恰好是被调制的正交分量，而其斜率等于高斯字母输出熵的负导数。这为膨胀的形成纠缠产生了一个支持下界；随后高斯最大熵和凹性给出了在高斯优化器处相切的全局上界。因此，衰减、放大、相位共轭和加性噪声基准信道的已知高斯公式在每个输入能量下对无限制集合都是精确的。通过被动输入基准分解和能量受限连续性，该结果扩展到每个单模高斯信道，包括低秩规范极限。未假设信道使用间的加性。
英文摘要
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.
