论文标题
高斯最大化器的证明猜想了噪音杂项测量的通信能力
Proof of the Gaussian maximizers conjecture for the communication capacity of noisy heterodyne measurements
论文作者
论文摘要
基于最近开发的凸编程框架[Arxiv：2204.10626]，我们为长期存在的猜想提供了关于高斯范围的最佳性质的长期猜想，以实现振荡器能量约束下广义异差接收器的最终通信速率。我们的结果概括了先前的结果（在能量阈值条件的有效性的假设下获得），并显示出在此条件内外的最佳编码结构上存在巨大差异。在阈值之外的情况下，证明的核心是一种新的Log-Sobolev类型不等式，将广义WEHRL熵与波函数梯度联系起来。
Basing on recently developed convex programming framework in the paper [arXiv:2204.10626], we provide a proof for a long-standing conjecture on optimality of Gaussian encondings for the ultimate communication rate of generalized heterodyne receivers under the oscillator energy constraint. Our results generalize previous ones (obtained under the assumption of validity of the energy threshold condition) and show a drastic difference in the structure of the optimal encoding within and beyond this condition. The core of the proof in the case beyond the threshold is a new log-Sobolev type inequality, which relates the generalized Wehrl entropy with the wavefunction gradient.
