quantum-minimax-estimation

name	quantum-minimax-estimation
description	Minimax estimation of high-order functionals using quantum computing arguments. Bridges quantum information theory with statistical estimation theory, providing sample-optimal bounds for functional estimation. Activation: minimax estimation, quantum arguments, high-order functionals, statistical estimation, quantum information theory, sample complexity, functional estimation, quantum statistics
metadata	{"arxiv_id":"2607.07540","published":"2026-07-07","authors":"Qisheng Wang","tags":["quantum","statistics","estimation","information-theory"]}

Quantum Minimax Estimation

Minimax estimation methodology for high-order functionals using quantum computing arguments (arXiv:2607.07540).

Core Methodology

• Formulate statistical functional estimation as a quantum state discrimination problem
• Leverage quantum query complexity lower bounds to establish minimax rates
• Use quantum amplitude estimation for accelerated functional estimation
• Connect quantum information geometry (Bures metric, fidelity) with classical statistical distance measures

Key Results

• Sample complexity bounds for estimating functionals of probability distributions using quantum arguments
• Tight upper and lower bounds matching up to constant factors
• Connections between quantum Fisher information and classical Cramer-Rao bounds for high-order functionals

When to Use

• Analyzing sample complexity of statistical estimators through quantum lens
• Designing quantum-accelerated statistical inference procedures
• Understanding fundamental limits of functional estimation
• Bridging quantum information theory with nonparametric statistics

Activation Keywords

• minimax estimation, quantum arguments, high-order functionals
• statistical estimation, sample complexity, quantum information
• functional estimation, quantum statistics, Bures metric