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Optimal von Neumann Entropy Estimation
Abstract
We show that the von Neumann entropy of an unknown d-dimensional quantum state ρ can be estimated to within additive error ε using Θ (d2/(εlog2(d)(1+εlog2(d))) + log2(d)/ε2) samples of ρ, matching the lower bound due to Wang (2026). Our estimator is based on a high-degree approximation polynomial and the main technical challenge is bounding its variance despite the large polynomial degree. We overcome this using a quantum Hoeffding decomposition, which preserves cancellations between different polynomial terms and reduces the analysis to derivative bounds for the approximation polynomial.
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BibTeX
@misc{chen2026optimal,
title = {{Optimal von Neumann Entropy Estimation}},
author = {Ziyun Chen and Minbo Gao and Qisheng Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.11151},
eprint = {2608.11151},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11151},
}
RIS
TY - UNPB
TI - Optimal von Neumann Entropy Estimation
AU - Ziyun Chen
AU - Minbo Gao
AU - Qisheng Wang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2608.11151
UR - https://arxiv.org/abs/2608.11151
AB - We show that the von Neumann entropy of an unknown d-dimensional quantum state ρ can be estimated to within additive error ε using Θ (d^2/(εlog^2(d)(1+εlog^2(d))) + log^2(d)/ε^2) samples of ρ, matching the lower bound due to Wang (2026). Our estimator is based on a high-degree approximation polynomial and the main technical challenge is bounding its variance despite the large polynomial degree. We overcome this using a quantum Hoeffding decomposition, which preserves cancellations between different polynomial terms and reduces the analysis to derivative bounds for the approximation polynomial.
ER -