标题： 经典广义纯度、熵和对数否定性的类比 显示英文标题

标题： Classical analogs of generalized purities, entropies, and logarithmic negativity

摘要： 最近提出了经典可积系统中纯度、线性量子熵和冯·诺依曼熵的经典类比，当相应的量子系统处于高斯态时。 我们通过提供经典可积系统的广义纯度、Bastiaans-Tsallis熵、Rényi熵和对数negativity的经典类比来推广这些结果。 这些经典类比完全由经典协方差矩阵表征。 我们在线性耦合谐振子、广义谐振子链和一维环形振子晶格的情况下精确计算了这些经典类比。 在所有这些系统中，当系统处于高斯态时，经典类比再现了其量子对应的结果。 在此背景下，我们的结果表明，高斯态的量子信息可以通过经典信息再现。 显示英文摘要

摘要： It has recently been proposed classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the corresponding quantum system is in a Gaussian state. We generalized these results by providing classical analogs of the generalized purities, Bastiaans-Tsallis entropies, R\'enyi entropies, and logarithmic negativity for classical integrable systems. These classical analogs are entirely characterized by the classical covariance matrix. We compute these classical analogs exactly in the cases of linearly coupled harmonic oscillators, a generalized harmonic oscillator chain, and a one-dimensional circular lattice of oscillators. In all of these systems, the classical analogs reproduce the results of their quantum counterparts whenever the system is in a Gaussian state. In this context, our results show that quantum information of Gaussian states can be reproduced by classical information.