全对称高斯态的真正多熵
Genuine Multi-Entropy of Fully Symmetric Gaussian States
浏览论文内容
中文总结 AI 辅助
本文研究全对称高斯态的三体真正Rényi多熵，给出精确结果和渐近公式，证明$n=2$时为零，并探讨与Haar随机态的异同。
中文摘要 AI 辅助
我们研究了全对称高斯态的三体真正Rényi多熵，作为压缩参数的函数，针对不同总玻色子模式数和不同子系统配置。对于少数模式，我们获得了精确结果，并推测了在大压缩参数极限下的渐近公式，该公式是副本指数$n$的函数，同时我们还发现了在特定三分割下$n=3$时的次领头子系统大小依赖项。我们解析地证明了任何纯玻色子高斯态的真正$n=2$ Rényi多熵对于任意模式数和任意三分割均为零。此外，为了研究对子系统大小的依赖，我们在保持总模式数固定的情况下，绘制了真正Rényi多熵作为子系统中模式数函数的曲线。我们讨论了这一结果与Haar随机态多熵曲线研究之间的异同。特别是，我们识别了一个与蒸发黑洞中多熵时间相关的子系统大小配置，在该配置下真正多熵的行为发生变化。
英文摘要
We study the tri-partite genuine Rényi multi-entropy of fully symmetric Gaussian states as a function of the squeezing parameter for different total number of bosonic modes under different subsystem configurations. Exact results for a few modes are obtained, and we conjecture an asymptotic formula at the limit of large squeezing parameter as a function of the replica index $n$, while also finding subleading subsystem-size dependent terms for $n=3$ under a specific tripartition. We analytically show that the genuine $n=2$ Rényi multi-entropy of any pure bosonic Gaussian states is zero for any number of modes and for any tripartition. Furthermore, to investigate the dependence on subsystem size, we plot the curve of genuine Rényi multi-entropy as a function of the number of modes in the subsystems while keeping the total number of modes fixed. We discuss differences and similarities between this result and studies of the multi-entropy curve for Haar random states. In particular, we identify a subsystem size configuration related with the multi-entropy time in an evaporating black hole for which the behavior of the genuine multi-entropy changes.
发表机构
- National Center for Theoretical Sciences, National Taiwan University（台湾大学国家理论科学中心）
- Department of Physics, National Sun Yat-sen University（国立中山大学物理系）
- National Institute of Technology, Yuge College（国立技术研究所育智学院）
机构由 AI 辅助整理，请以论文原文为准。
