Uniform Hiding and Two Routes to Relative Accuracy in Gaussian Boson Sampling

Hongru Zhao

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arXiv · 2609.01008

Uniform Hiding and Two Routes to Relative Accuracy in Gaussian Boson Sampling

Hongru Zhao

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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.

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Hongru Zhao. 2026-09-11. Uniform Hiding and Two Routes to Relative Accuracy in Gaussian Boson Sampling. https://arxiv.org/abs/2609.01008

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