发表机构
University of Waterloo; Perimeter Institute for Theoretical Physics; Concordia University; Syracuse University（滑铁卢大学; 珀蒂默理论物理研究所; 康考迪亚大学; 雪城大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究量子信道最小输出 \(p -\) 雷尼熵可加性问题，通过结合两种随机投影构造，证明对于 \(p > 3/4\) 或 \(0\leq p < 1/4\) 存在反例，缩小未解决区间并改进输出维度阈值。
AI 中文摘要
最小输出熵的可加性是量子信息论中的核心问题。对于每个 \(p > 1\) 的雷尼阶、冯·诺依曼点 \(p = 1\) 以及接近 \(p = 0\) 时，已知存在非可加性，而 \(0 < p < 1\) 的大部分区间仍未解决。我们证明，对于每个满足 \(p > 3/4\) 或 \(0\leq p < 1/4\) 的雷尼阶 \(p\)，存在有限维投影诱导的量子信道，使得最小输出 \(p -\) 雷尼熵的可加性不成立。证明结合了两种相关的随机投影构造：对于 \(p > 3/4\) 的乘积共轭贝尔态见证和对于 \(p < 1/4\) 的转置补秩缺陷见证。因此，\(0 < p < 1\) 中未解决的部分缩小到 \([1/4, 3/4]\)。我们的估计还改进了最小输出冯·诺依曼熵可加性违反的输出维度阈值，该阈值最初由贝林斯基、柯林斯和根田建立。
英文摘要
The additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every Rényi order $p>1$, at the von Neumann point $p=1$, and for sufficiently small positive $p$, while much of the interval $0<p<1$ has remained open. In this work, we prove that for every $p>0$ there exist finite-dimensional quantum channels whose minimum output $p$-Rényi entropies violate additivity. Our proof combines two constructions: random projection-induced channels yield nonadditivity for $p>3/4$, and antisymmetric postprocessing extends the violation to all positive Rényi orders. Our estimates also improve the output-dimension bound obtained by Belinschi, Collins, and Nechita for additivity violation of minimum output von Neumann entropy.
