Anticoncentration and entanglement in Gaussian boson sampling
Abstract
Anticoncentration and entanglement are two properties used to study classical hardness or easiness of Gaussian boson sampling in varying regimes. In this paper, we consider three directions concerning anticoncentration and entanglement in Gaussian boson sampling: (1) We derive closed-form expressions for the second moment of hafnians of symmetric Gaussian products, and use this to precisely locate the anticoncentration transition as a function of the number of squeezed input modes. (2) We derive closed-form expressions for the Rényi-α Page curves for Gaussian boson sampling. (3) We study unequal input squeezing parameters (si)i, and prove estimates as well as monotonicity of the average-case Rényi-2 entropy Page curve in terms of the magnitudes |si|, which allow for extending equal squeezing results to unequal squeezing.
Related
- Local Anticoncentration for Gaussian Boson Sampling via Conditional Wishart Geometry
- Log-depth entanglement transition in hypercube Gaussian boson sampling
- Anticoncentration of Complex Gaussian Hafnians
- Shifted Anticoncentration for Real Gram Hafnians and Symmetric Gaussian Hafnians
- Polynomial-time classical simulation of boson and fermion sampling under thermal loss
BibTeX
@misc{shou2026anticoncentration,
title = {{Anticoncentration and entanglement in Gaussian boson sampling}},
author = {Laura Shou and Adam Ehrenberg and Yu-Xin Wang and Joseph T. Iosue and Alexey V. Gorshkov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01241},
eprint = {2609.01241},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01241},
}
RIS
TY - UNPB
TI - Anticoncentration and entanglement in Gaussian boson sampling
AU - Laura Shou
AU - Adam Ehrenberg
AU - Yu-Xin Wang
AU - Joseph T. Iosue
AU - Alexey V. Gorshkov
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01241
UR - https://arxiv.org/abs/2609.01241
AB - Anticoncentration and entanglement are two properties used to study classical hardness or easiness of Gaussian boson sampling in varying regimes. In this paper, we consider three directions concerning anticoncentration and entanglement in Gaussian boson sampling: (1) We derive closed-form expressions for the second moment of hafnians of symmetric Gaussian products, and use this to precisely locate the anticoncentration transition as a function of the number of squeezed input modes. (2) We derive closed-form expressions for the Rényi-α Page curves for Gaussian boson sampling. (3) We study unequal input squeezing parameters (s_i)_i, and prove estimates as well as monotonicity of the average-case Rényi-2 entropy Page curve in terms of the magnitudes |s_i|, which allow for extending equal squeezing results to unequal squeezing.
ER -