Quantum-Optimal Frequency Estimation of Stochastic AC Fields

TL;DR

This paper establishes the quantum limits for frequency estimation of stochastic AC fields, demonstrating how entanglement and specific quantum states can enhance precision beyond classical bounds.

Contribution

It maps frequency estimation to quantum channel estimation, deriving exact quantum Fisher information bounds and showing how entangled states improve measurement precision.

Findings

Quantum Fisher information bounds for stochastic field frequency estimation.

Superpositions of Dicke states achieve the bounds in certain regimes.

GHZ states improve precision over unentangled states, achieving Heisenberg scaling.

Abstract

Resolving frequencies in a time-dependent field is classically limited by the measurement bandwidth. Using tools from quantum metrology and quantum control may overcome this limit, yet the full advantage afforded by entanglement so far remains elusive. Here we map the problem of frequency measurement to that of estimating a global dephasing quantum channel. In this way, we determine the ultimate quantum limits of {frequency estimation in stochastic AC} sensing. We find exact {quantum Fisher information bounds} for estimating frequency and frequency differences of stochastic fields. In particular, given two close signals with frequency separation $\omega_r$, we find that the quantum Fisher information (QFI) for the separation estimation is approximately $2/\omega_r^2$, {i.e.}~\emph{inversely} proportional to the separation parameter. The bounds are achievable in certain regimes by superpositions of Dicke states. GHZ states are suboptimal but improve precision over unentangled states, achieving Heisenberg scaling in the low-bandwidth limit. This work establishes a robust framework for stochastic AC signal sensing that can be extended to arbitrary time-dependent and stochastic fields.