New bounds on adaptive quantum metrology under Markovian noise

TL;DR

This paper derives new, more general bounds on the quantum Fisher information growth rate for parameter estimation in noisy quantum systems, applicable to various settings including time-dependent and infinite-dimensional systems, and explores implications for measurement sensitivity.

Contribution

It introduces tighter, more broadly applicable bounds on quantum Fisher information growth under Markovian noise, derived directly from the stochastic master equation without discretization.

Findings

Bounds apply to time-dependent Hamiltonians and Lindblad operators

Sensitivity bandwidth relates to quantum fluctuations of H/g

Non-classical states can enhance sensitivity range

Abstract

We analyse the problem of estimating a scalar parameter $g$ that controls the Hamiltonian of a quantum system subject to Markovian noise. Specifically, we place bounds on the growth rate of the quantum Fisher information with respect to $g$, in terms of the Lindblad operators and the $g$-derivative of the Hamiltonian $H$. Our new bounds are not only more generally applicable than those in the literature -- for example, they apply to systems with time-dependent Hamiltonians and/or Lindblad operators, and to infinite-dimensional systems such as oscillators -- but are also tighter in the settings where previous bounds do apply. We derive our bounds directly from the stochastic master equation describing the system, without needing to discretise its time evolution. We also use our results to investigate how sensitive a single detection system can be to signals with different time dependences. We demonstrate that the sensitivity bandwidth is related to the quantum fluctuations of $\partial H/\partial g$, illustrating how 'non-classical' states can enhance the range of signals that a system is sensitive to, even when they cannot increase its peak sensitivity.