Precision Limits of Multiparameter Markovian-Noise Metrology

TL;DR

This paper establishes fundamental precision bounds for multiparameter quantum noise estimation in Markovian systems, revealing super-Heisenberg scaling under certain conditions and proposing optimal measurement protocols.

Contribution

It introduces the ultimate precision limits for multiparameter Markovian noise metrology, including a practical protocol achieving these bounds in specific regimes.

Findings

Precision bounds scale as Ω(1/(TR^2)) with sensing time T and channels R.

Super-Heisenberg scaling with system size N for collective k-body dissipation.

Rapid Prepare-and-Measure protocol attains these limits by tracking quantum jumps.

Abstract

Measuring stochastic signals ("noise metrology") constitutes a central task in quantum sensing and the characterization of open quantum systems. Here we establish ultimate precision bounds for multiparameter estimation of stochastic signals encoded through Markovian Lindblad dynamics, allowing for arbitrary quantum control and noiseless ancillae. Although Markovianity enforces standard-quantum-limit scaling with sensing time $T$, our bounds reveal Heisenberg-type scaling in the number of dissipative channels, $R$: when the stochastic signal exhibits high-rank correlations across the $R$ channels and the probe is entangled, the average variance (per parameter) scales no better than $\Omega(1/(TR^2))$. For collective $k$-body dissipation, $R=\Theta(N^k)$, signifying super-Heisenberg scaling with the system size $N$. We further show that, when the unknown parameters enter through the dissipative eigenrates, a Rapid Prepare-and-Measure (RPM) protocol that tracks many distinct quantum jumps in parallel attains these limits. In this regime, the estimation problem reduces to a multi-Poisson counting model, providing a conceptually clean route to optimal quantum noise metrology. We illustrate the breadth of the framework with applications to networked noise metrology, collective many-body dissipation, learning Pauli noise, and subdiffraction quantum imaging.