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