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arXiv 2301.09074quant-phhep-th
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随机纯态中子系统的平均Rényi熵

Average Rényi Entropy of a Subsystem in Random Pure State

MuSeong Kim, Mi-Ra Hwang, Eylee Jung, DaeKil Park

备注：
14 pages, 3 figures, will appear in QIP
发表信息：
Quantum Inf. Proc.23 (2024) 37
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AI总结：

本文解析计算了随机纯态中子系统的平均Rényi熵，并发现量子信息消失区域随α增大而缩短直至消失。

摘要：

本文研究了当整个复合系统AB处于随机纯态时，子系统A的平均Rényi熵$S_α$。我们假设A和AB的希尔伯特空间维度分别为$m$和$m n$。首先，我们在$m = α= 2$的情况下解析地计算了平均Rényi熵。我们将此解析结果与近似平均Rényi熵进行比较，结果显示两者非常接近。对于一般情况，我们解析地计算了近似Rényi熵$\tilde{S}_α (m,n)$的平均值。当$1 \nll n$时，$\tilde{S}_α (m,n)$简化为$\nln m - \frac{α}{2 n} (m - m^{-1})$，这与平均冯·诺依曼熵的渐近表达式一致。基于$\tilde{S}_α (m,n)$的解析结果，我们绘制了由$\tilde{S}_α (m,n)$导出的量子信息的$\nln m$依赖性。值得注意的是，信息的近乎消失区域随着$α$的增大而缩短，并最终在$α\rightarrow \ninfty$的极限下消失。文中简要讨论了该结果的物理意义。

英文摘要：

In this paper we examine the average Rényi entropy $S_α$ of a subsystem $A$ when the whole composite system $AB$ is a random pure state. We assume that the Hilbert space dimensions of $A$ and $AB$ are $m$ and $m n$ respectively. First, we compute the average Rényi entropy analytically for $m = α= 2$. We compare this analytical result with the approximate average Rényi entropy, which is shown to be very close. For general case we compute the average of the approximate Rényi entropy $\widetilde{S}_α (m,n)$ analytically. When $1 \ll n$, $\widetilde{S}_α (m,n)$ reduces to $\ln m - \fracα{2 n} (m - m^{-1})$, which is in agreement with the asymptotic expression of the average von Neumann entropy. Based on the analytic result of $\widetilde{S}_α (m,n)$ we plot the $\ln m$-dependence of the quantum information derived from $\widetilde{S}_α (m,n)$. It is remarkable to note that the nearly vanishing region of the information becomes shorten with increasing $α$, and eventually disappears in the limit of $α\rightarrow \infty$. The physical implication of the result is briefly discussed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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