AI 中文总结
该研究证明最小输出Rényi熵可加性可在所有非负阶数同时违反近一位，通过自由群构造和Haagerup估计实现，并给出最优输出维数尺度。
AI 中文摘要
我们证明最小输出Rényi熵可加性可以在每个非负阶数上同时失败近一位。对于每个$\varepsilon\in(0,\log2)$，存在一个具有实Stinespring等距的有限维量子信道，使得相同的最大纠缠输入对所有$p\in[0,\infty]$见证至少$\log2-\varepsilon$的张量平方熵间隙。输出维数可以选为$O(\varepsilon^{-3})$当$\varepsilon\downarrow0$。该构造使用自由群的直积：张量化Haagerup估计控制单拷贝输出，而不同因子之间的交换性强制在两拷贝时发生精确的Bell分支碰撞。强收敛给出了通过右角Artin群的有限维表示后接实化的存在性实现，以及一个Haar正交模型，其成功概率随矩阵维数增长趋于1。我们还确定了精确的Bell商，证明了渐近尖锐的正则半径界，并表明在当前纯度-秩证书内三次输出维数尺度是最优的。
英文摘要
We prove that minimum-output Rényi-entropy additivity can fail by almost one bit simultaneously at every nonnegative order. For every $\varepsilon\in(0,\log2)$, there exists a finite-dimensional quantum channel with a real Stinespring isometry such that the same maximally entangled input witnesses a tensor-square entropy gap of at least $\log2-\varepsilon$ for all $p\in[0,\infty]$. The output dimension can be chosen to be $O(\varepsilon^{-3})$ as $\varepsilon\downarrow0$. The construction uses direct products of free groups: tensorized Haagerup estimates control the one-copy outputs, while commutation between distinct factors forces exact Bell-branch collisions at two copies. Strong convergence gives both an existential realization through finite-dimensional representations of right-angled Artin groups followed by realification, and a Haar-orthogonal model whose success probability tends to one as the matrix dimension grows. We also determine the exact Bell quotient, prove asymptotically sharp regular-radius bounds, and show that the cubic output-dimension scale is optimal within the present purity--rank certificate.
Comments34 pages, 1 figure
