Information geometry under hierarchical quantum measurement

TL;DR

This paper develops a framework to analyze how hierarchical quantum measurements distort quantum information, providing bounds on the Fisher information discrepancy and implications for quantum metrology.

Contribution

It introduces analytical bounds on the Fisher information difference under hierarchical p-local quantum measurements, unifying and extending existing results.

Findings

Bounds on quantum-classical Fisher information discrepancy

Implications for multi-parameter quantum metrology precision limits

Unified framework encompassing various measurement scenarios

Abstract

In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The characterization of the discrepancy is an important subject in quantum information science, which plays a key role in understanding the difference between the structures of the quantum and classical information. Here we analyze the discrepancy in terms of the Fisher information metric and present a framework that can provide analytical bounds on the difference under hierarchical quantum measurements. Specifically, we present a set of analytical bounds on the difference between the quantum and classical Fisher information metric under hierarchical p-local quantum measurements, which are measurements that can be performed collectively on at most p copies of quantum states. The results can be directly transformed to the precision limit in multi-parameter quantum metrology, which leads to characterizations of the tradeoff among the precision of different parameters. The framework also provides a coherent picture for various existing results by including them as special cases.