PreprintCC BY 4.0arXiv
Uniform Hiding and Two Routes to Relative Accuracy in Gaussian Boson Sampling
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 N2/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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BibTeX
@misc{zhao2026uniform,
title = {{Uniform Hiding and Two Routes to Relative Accuracy in Gaussian Boson Sampling}},
author = {Hongru Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01008},
eprint = {2609.01008},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01008},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uniform Hiding and Two Routes to Relative Accuracy in Gaussian Boson Sampling
AU - Hongru Zhao
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.01008
UR - https://arxiv.org/abs/2609.01008
AB - 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.
ER -