Critical quantum metrology assisted by real-time feedback control

TL;DR

This paper explores how adaptive real-time feedback control can enable quantum metrology near critical points to surpass classical precision limits, even with limited measurements and prior knowledge.

Contribution

It introduces a no-go theorem for non-adaptive strategies and demonstrates that adaptive feedback can achieve quantum-enhanced precision in many-body systems.

Findings

Non-adaptive strategies fail to exploit quantum critical enhancement with large N and limited prior knowledge.

Adaptive strategies with real-time feedback can attain sub-shot noise scaling.

Demonstrated improved estimation in spin chains and Bose-Hubbard lattices.

Abstract

We investigate critical quantum metrology,that is the estimation of parameters in many-body systems close to a quantum critical point, through the lens of Bayesian inference theory. We first derive a no-go result stating that any non-adaptive measurement strategy will fail to exploit quantum critical enhancement (i.e. precision beyond the shot-noise limit) for a sufficiently large number of particles $N$ whenever our prior knowledge is limited. We then consider different adaptive strategies that can overcome this no-go result, and illustrate their performance in the estimation of (i) a magnetic field using a probe of 1D spin Ising chain and (ii) the coupling strength in a Bose-Hubbard square lattice. Our results show that adaptive strategies with real-time feedback control can achieve sub-shot noise scaling even with few measurements and substantial prior uncertainty.