发表机构
Thrust of Artificial Intelligence, Information Hub,The Hong Kong University of Science and Technology (Guangzhou); Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（香港科技大学（广州）信息枢纽人工智能领域; 粤港澳大湾区量子科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们通过自由群直积和高围长图构造量子信道，在任意正Rényi阶上实现任意大的最小输出熵可加性违背，且输出量子比特数更少。
AI 中文摘要
我们给出了一种闭式的有限维量子信道构造，其具有实数代数矩阵元，并表现出对最小输出Rényi熵可加性的任意大违背，该违背在任意给定的正Rényi阶之上均匀成立，该构造基于自由群的直积和固定域高围长图的不同有限实现。更精确地，对于每个$p_0>0$和$g>0$，我们构造一个信道和一个Bell输入，使得对于所有$p\in[p_0,\infty]$，可加性间隙同时大于$g$。令$r=\lceil2g\rceil$，该构造使用$15r$个输出量子比特和$O(r2^{30r}+r^2(1+p_0^{-1}))$个输入量子比特。与Shou和Gorshkov\cite{ShouGorshkov2026}所给出的参数相比，对于每个目标间隙，我们的构造使用更少的输出量子比特，并且在正截止固定时随着间隙增大，其渐近输入量子比特上界更小。在von Neumann阶，一个单独的专门化给出了一个显式信道，其间隙大于$1/1024$，使用$37608898$个输入量子比特和$8$个输出量子比特。
英文摘要
We give a closed-form finite-dimensional construction of quantum channels with real algebraic entries exhibiting arbitrarily large violations of minimum-output Rényi entropy additivity uniformly above any prescribed positive Rényi order, using a different finite realization based on direct products of free groups and fixed-field high-girth graphs. More precisely, for every $p_0>0$ and $g>0$, we construct one channel and one Bell input for which the additivity gap is greater than $g$ simultaneously for all $p\in[p_0,\infty]$. With $r=\lceil2g\rceil$, the construction uses $15r$ output qubits and $O(r2^{30r}+r^2(1+p_0^{-1}))$ input qubits. Compared with the stated parameters of Shou and Gorshkov \cite{ShouGorshkov2026}, our construction uses fewer output qubits for every target gap and has a smaller asymptotic input-qubit bound as the gap grows with the positive cutoff fixed. At the von Neumann order, a separate specialization gives an explicit channel with gap greater than $1/1024$ using $37608898$ input qubits and $8$ output qubits.
Comments39 pages, 1 figure
