Uncertain Quantum Critical Metrology: From Single to Multi Parameter Sensing

TL;DR

This paper develops a framework to analyze how uncertainties in control parameters affect the sensitivity and robustness of critical quantum sensors, especially near quantum phase transitions, with practical implications for quantum metrology.

Contribution

It introduces a systematic approach to evaluate the impact of control parameter uncertainties on critical quantum metrology, bridging single- and multi-parameter estimation.

Findings

Uncertainty in control parameters can significantly reduce quantum advantage.

A fundamental trade-off exists between robustness and sensitivity in finite systems.

The framework is applied to Ising and Lipkin-Meshkov-Glick models.

Abstract

Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the parameters of the Hamiltonian. In realistic settings, there is always some degree of uncertainty in the control parameters used to tune the system to criticality. These uncertainties, while not the target of estimation, can significantly affect the attainable precision, effectively acting as nuisance parameters in the estimation process. Despite being a practically relevant source of noise, their impact on critical metrology has been largely overlooked. In this work we present a general framework that interpolates between single- and multiparameter estimation settings, enabling a systematic analysis of how such uncertainties influence sensitivity. We apply this framework to the paradigmatic transverse field Ising and Lipkin-Meshkov-Glick models, explicitly demonstrating how uncertainty in control parameters affects the metrological performance of critical sensors. For finite-size systems, we identify a fundamental trade-off between robustness to uncertainty and the ability to retain a quantum advantage at the critical point. Our results contribute to a deeper understanding of the practical limitations of critical quantum metrology and provide a route toward its more resilient implementation.