Quantum Metrology Subject to Instrumentation Constraints

TL;DR

This paper formulates the problem of optimizing quantum parameter estimation precision under instrumentation constraints as convex linear programs, providing analytical solutions for average case scenarios and illustrating the impact of constraints through an example.

Contribution

It introduces a convex optimization framework for quantum metrology with instrumentation constraints, including analytical solutions for average case optimization.

Findings

Optimization problems are linear programs.

Analytical solutions for average case optimization.

Constraints reduce achievable precision compared to ideal Quantum Fisher Information.

Abstract

Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and average case objective for optimizing the precision. Focusing on the single parameter case, we show that the optimization problems are {\em linear programs}. For the average case the solution to the linear program can be expressed analytically and involves a simple search: finding the largest element in a list. An example is presented which compares what is possible under constraints against the ideal with no constraints, the Quantum Fisher Information.