发表机构
Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为离散量子卷积的冯·诺依曼熵建立次模框架，证明熵增益的多拟阵几何，导出卷积强次可加性、量子Ruzsa三角不等式及Plünnecke--Ruzsa不等式，将加性组合学次模方法引入量子领域。
AI 中文摘要
我们为离散量子卷积的冯·诺依曼熵建立了一个次模框架，提供了熵加性组合学直接方向的非交换对应物。我们首先引入全局加权量子卷积，它们构成由固定输入集合的容许子集索引的相容族。我们的主定理揭示了其熵增长背后的多拟阵几何：相对于任何固定的容许输入块，熵增益对剩余输入的所有子集都允许一个归一化的、单调的、次模的扩展。该定理导出了卷积强次可加性、量子Ruzsa三角不等式以及任意输入态的量子熵Plünnecke--Ruzsa不等式。对于重复输入，它给出了容许尺度上熵增长的尖锐比较；特别是，量子加倍常数以最优指数控制所有更高阶的容许卷积熵。总之，这些结果将加性组合学中的次模方法引入量子环境，并为广泛的卷积熵不等式族提供了一条系统途径。
英文摘要
We develop a submodular framework for the von Neumann entropy of discrete quantum convolutions, providing a noncommutative counterpart to the direct side of entropic additive combinatorics. We first introduce globally weighted quantum convolutions, which form compatible families indexed by admissible subsets of a fixed collection of inputs. Our main theorem reveals a polymatroidal geometry underlying their entropy growth: relative to any fixed admissible input block, the entropy gains admit a normalized, monotone, submodular extension to all subsets of the remaining inputs. The theorem yields convolutional strong subadditivity, quantum Ruzsa triangle inequality, and quantum entropic Plünnecke--Ruzsa inequalities for arbitrary input states. For repeated inputs, it gives sharp comparisons of entropy growth across admissible scales; in particular, the quantum doubling constant controls all higher admissible convolution entropies with optimal exponents. Together, these results bring submodular methods from additive combinatorics into the quantum setting and provide a systematic route to broad families of convolutional entropy inequalities.
