On Asymptotic Quantum Statistical Inference

TL;DR

This paper investigates asymptotic quantum statistical inference for multiple identical quantum systems, employing classical and advanced quantum statistical methods to establish optimality results.

Contribution

It introduces a novel combination of classical van Trees inequality and quantum Local Asymptotic Normality for quantum state estimation.

Findings

Derives asymptotic bounds for quantum state estimation accuracy

Connects classical and quantum statistical inference methods

Provides theoretical foundations for optimal quantum measurements

Abstract

We study asymptotically optimal statistical inference concerning the unknown state of $N$ identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather more sophisticated approach using the recently developed quantum form of LeCam's theory of Local Asymptotic Normality.