发表机构
School of Statistics, University of Minnesota（明尼苏达大学统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文通过条件 Wishart 几何证明了高斯玻色采样中 hafnian 的局部反集中界，为有限 Haar 干涉仪提供了理论保证。
AI 中文摘要
局部反集中控制着高斯玻色采样中加性输出概率估计向相对估计的转换。我们证明了对于 $2n$ 个选定模式，复高斯转置 Gram 矩阵的 hafnian 满足中心均匀二次小球界，其显式有限系数在高斯行数至少为 $n^2/\log n$ 量级时呈多项式增长。当高斯行数趋于无穷时，独立复对称高斯系综满足反集中性质。对于转置 Gram hafnian 界，证明通过傅里叶插值压缩相依的 hafnian 余因子，并通过保持转置 Gram 坐标的条件 Wishart 恒等式控制其自耦合方差。独立扰动满足相关界，正混合密度表明局部二次幂是精确的。结合配套论文中的均匀隐藏定理，该结果为有限 Haar 干涉仪提供了局部反集中性。
英文摘要
Local anticoncentration controls the conversion of additive output probability estimates to relative estimates in Gaussian boson sampling. We prove a center-uniform quadratic small-ball bound for hafnians of complex Gaussian transpose Gram matrices for $2n$ selected modes, with an explicit finite coefficient that is polynomial when the number of Gaussian rows is at least of order $n^2/\log n$. Letting the Gaussian row count tend to infinity yields anticoncentration for the independent complex symmetric Gaussian ensemble. For the transpose Gram hafnian bound, the proof compresses dependent hafnian cofactors by Fourier interpolation and controls their self-coupled variance through a conditional Wishart identity that preserves the transpose Gram coordinate. Independent perturbations satisfy related bounds, and a positive mixture density shows that the local quadratic power is exact. Together with the uniform hiding theorem in the companion paper, the result gives local anticoncentration for finite Haar interferometers.
Comments39 pages, 4 figures, 1 table. Includes all appendices
