Optimal Control for Quantum Metrology via Pontryagin's principle

TL;DR

This paper formulates quantum metrology as an optimal control problem and uses Pontryagin's Maximum Principle to find protocols that maximize quantum Fisher information, improving parameter estimation precision.

Contribution

It introduces a novel optimal control framework for quantum metrology using Pontryagin's principle, including an augmented system for Fisher information derivatives.

Findings

Derived necessary conditions for optimal quantum metrology protocols.

Generalized the formalism to include control constraints.

Applicable to maximizing classical Fisher information as well.

Abstract

Quantum metrology comprises a set of techniques and protocols that utilize quantum features for parameter estimation which can in principle outperform any procedure based on classical physics. We formulate the quantum metrology in terms of an optimal control problem and apply Pontryagin's Maximum Principle to determine the optimal protocol that maximizes the quantum Fisher information for a given evolution time. As the quantum Fisher information involves a derivative with respect to the parameter which one wants to estimate, we devise an augmented dynamical system that explicitly includes gradients of the quantum Fisher information. The necessary conditions derived from Pontryagin's Maximum Principle are used to quantify the quality of the numerical solution. The proposed formalism is generalized to problems with control constraints, and can also be used to maximize the classical Fisher information for a chosen measurement.