Preferred Measurements: Optimality and Stability in Quantum Parameter Estimation

TL;DR

This paper introduces a formalism for quantum parameter estimation, focusing on optimality and stability, and presents the concept of information complement to analyze measurement precision and system properties.

Contribution

It introduces the concept of information complement and analyzes measurement stability, revealing conditions for optimal precision in quantum measurements.

Findings

Maximally precise measurements can be independent of the true parameter value.

Optimal measurement stability can be quantified by the curvature of the information complement.

Restrictions on probe states and dynamics are necessary for achieving optimal precision.

Abstract

We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of `information complement' is introduced. It undermines measurement precision and its minimization reveals the system properties at an optimal point. Maximally precise measurements can exhibit independence from the true value of the estimated parameter, but demanding this severely restricts the type of viable probe and dynamics, including the requirement that the Hamiltonian be block-diagonal in a basis of preferred measurements. The curvature of the information complement near a globally optimal point provides a new quantification of measurement stability.