Nonlinear quantum metrology of many-body open systems

TL;DR

This paper establishes bounds on parameter estimation errors in nonlinear quantum metrology for many-body open systems, demonstrating how entanglement and many-body effects can surpass classical limits in precision.

Contribution

It introduces general bounds for estimation error scaling in nonlinear quantum metrology of many-body open systems, highlighting the role of entanglement and interaction range.

Findings

Estimation error scales as N^{-(k - p/2)} for GHZ states, surpassing shot-noise limit when 2k > p+1.

System-environment coupling can be estimated with precision N^{-p/2}.

Long-range Ising model shows enhanced precision below a certain interaction range threshold.

Abstract

We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a $k$-body Hamiltonian and $p$-body Lindblad operators, the estimation error of a Hamitonian parameter using a Greenberger-Horne-Zeilinger (GHZ) state as a probe is shown to scale as $N^{-\left(k-\frac{p}{2}\right)}$, surpassing the shot-noise limit for $2k>p+1$. Metrology equivalence between initial product states and maximally entangled states is established for $p\geq 1$. We further show that one can estimate the system-environment coupling parameter with precision $N^{-\frac{p}{2}}$, while many-body decoherence enhances the precision to $N^{-k}$ in the noise-amplitude estimation of a fluctuating $k$-body Hamiltonian. For the long-range Ising model we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.