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
该研究针对高斯玻色采样中Haar干涉仪的矩形块形成的复对称转置Gram矩阵，证明其与复高斯转置Gram律的有限总变差比较，误差界明确，为高斯玻色采样硬度论证提供随机矩阵替代分量。
AI 中文摘要
具有等压缩有效输入的高斯玻色采样（Gaussian boson sampling），通过由Haar干涉仪的矩形块形成的复对称转置Gram矩阵分配无碰撞概率。我们证明了其与对应复高斯转置Gram律的有限总变差比较，误差界是明确的，与所选输出模式数成二次关系，与干涉仪大小成反比，且在压缩有效输入数量上是均匀的。证明结合了稠密区的中心圆正交系综（centered circular orthogonal ensemble）得分分析与矩形相对熵界。该结果为高斯玻色采样硬度论证提供了随机矩阵替代分量。
英文摘要
Gaussian boson sampling requires control of how closely finite optical matrices follow Gaussian reference laws. We prove an explicit total variation bound of order $N^2/M$ between a rescaled Haar transpose Gram block and its Gaussian transpose Gram counterpart, where $N$ is the detected photon count and $M$ is the number of optical modes. The bound establishes quantitative product hiding uniformly over every number of squeezed inputs. The proof combines Stiefel recursion, centered circular orthogonal ensemble scores, and a rectangular entropy estimate. Applications combine hiding with local hafnian bounds to obtain relative probability guarantees and connect them to sampler error through exact photon-sector normalization.
Comments49 pages, 5 figures, 4 tables
