Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling

TL;DR

This paper analyzes how quantum Fisher information scales in critical quantum metrology protocols, revealing universal regimes and bounds applicable to finite-time and finite-size systems, especially in fully-connected models.

Contribution

It provides a comprehensive analysis connecting static and dynamical approaches in critical quantum metrology, unveiling universal scaling regimes and deriving a general precision bound.

Findings

Universal precision-scaling regimes identified

Finite-time and finite-size systems still achieve these regimes

Derived a general bound for quadratic Hamiltonians

Abstract

Phase transitions represent a compelling tool for classical and quantum sensing applications. It has been demonstrated that quantum sensors can in principle saturate the Heisenberg scaling, the ultimate precision bound allowed by quantum mechanics, in the limit of large probe number and long measurement time. Due to the critical slowing down, the protocol duration time is of utmost relevance in critical quantum metrology. However, how the long-time limit is reached remains in general an open question. So far, only two dichotomic approaches have been considered, based on either static or dynamical properties of critical quantum systems. Here, we provide a comprehensive analysis of the scaling of the quantum Fisher information for different families of protocols that create a continuous connection between static and dynamical approaches. In particular, we consider fully-connected models, a broad class of quantum critical systems of high experimental relevance. Our analysis unveils the existence of universal precision-scaling regimes. These regimes remain valid even for finite-time protocols and finite-size systems. We also frame these results in a general theoretical perspective, by deriving a precision bound for arbitrary time-dependent quadratic Hamiltonians.