| 摘要: |
| 研究了基于随机密度矩阵特征值联合分布的广义微分熵。首先，在罗莱珍等人的论文基础上，计算在Wishart矩阵特征值联合分布下的广义微分熵;然后，采用Laplace变换和Laplace逆变换来计算在随机量子态特征值联合分布下以及在随机密度矩阵对角线联合分布下的微分熵；另一方面，研究了由随机量子态所诱导的相关随机矩阵模型，该模型在量子信息理论中有着重要的作用；最后，以Renyi熵和Tsallis熵为例来验证在3种情形下的广义微分熵，并推广了罗莱珍等人的结果。 |
| 关键词: 广义微分熵 Renyi熵 Tsallis熵 |
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| The Generalized Differential Entropy Based on Joint Distribution of Eigenvalues of Random Density Matrix |
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LI Wan-qing,WANG Jia-mei,WANG Tian-tian
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| Abstract: |
| We study the generalized differential entropy based on the joint distribution of eigenvalues of random density matrices. First, based on the paper by Luo Laizhen et al., we calculate the generalized differential entropy under the joint distribution of eigenvalues of Wishart matrices. Then, we use Laplace transform and Laplace inverse transform to calculate the generalized differential entropy under the joint distribution of eigenvalues of random quantum states and the joint distribution of diagonals of random density matrices. On the other hand, the related random matrix model induced by the random quantum state is studied. This model plays an important role in quantum information theory. Finally, the Renyi entropy and Tsallis entropy are taken as examples to verify the generalized differential entropy in three cases, and we promote the results of Luo Laizhen et al. |
| Key words: the generalized differential entropy the Renyi entropy the Tsallis entropy |
