On the First Order Asymptotic Theory of Quantum Estimation

TL;DR

This paper develops a rigorous first order asymptotic theory for quantum estimation, avoiding Fisher information and MLE, and includes estimation of quantum states via LOCC and quantum operations.

Contribution

It introduces a new framework for quantum estimation theory that does not rely on Fisher information or MLE, and addresses state and operation estimation under LOCC.

Findings

Provides a rigorous foundation for quantum estimation asymptotics

Constructs optimal estimators based on locally unbiased estimators

Extends analysis to quantum state and operation estimation

Abstract

We give a rigorous treatment on the foundation of the first order asymptotic theory of quantum estimation, with tractable and reasonable regularity conditions. Different from past works, we do not use Fisher information nor MLE, and an optimal estimator is constructed based on locally unbiased estimators. Also, we treat state estimation by local operations and classical communications (LOCC), and estimation of quantum operations.