Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Zhao, Hongru
Institution: University of Minnesota
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206218153