Information Theoretical Analysis of Quantum Metrology

TL;DR

This paper develops an information-theoretic framework for quantum metrology, demonstrating how to maximize information extraction, connect it with traditional variance-based limits, and show entangled measurements are unnecessary for reaching the Heisenberg limit.

Contribution

It introduces an information-theoretic approach to quantum metrology, linking it with conventional methods and showing entangled measurements are not required for optimal precision.

Findings

Maximum information extraction via optimal state initialization and measurement.

Equivalence of information-theoretic and variance-based Heisenberg limits.

Entangled measurements are not necessary for achieving the Heisenberg limit.

Abstract

We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a quantum measurement at the end. Our analysis can apply to both the single-parameter and the multi-parameter estimation procedures as well as to any other quantum information processing procedures. We then establish a direct connection between the information-theoretic picture of quantum metrology and its conventional variance-covariance picture, by showing that any estimation procedure achieves Heisenberg limit in variance-covariance picture can also reach the information-theoretic Heisenberg limit in the asymptotic sense. As a direct consequence, we argue that the entangled measurement is not necessary for achieving Heisenberg limit in the information-theoretic pictures, which is explicitly illustrated for the Quantum-Classical parallel strategy of quantum metrology with a separable measurement employed and the Heisenberg limit saturated in both pictures.