Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

TL;DR

This paper investigates quantum frequency estimation using N-qubit probes under independent dephasing channels with continuous monitoring, deriving analytical solutions and showing how detection efficiency impacts quantum Fisher information.

Contribution

It provides analytical solutions for conditional states in monitored dephasing channels and reveals how detection efficiency affects quantum Fisher information in frequency estimation.

Findings

Perfect detection preserves noiseless QFI

Reduced detection efficiency lowers QFI to unmonitored levels

Analytical solutions for conditional states under continuous monitoring

Abstract

We discuss the problem of estimating a frequency via N-qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional states, for generic initial states and for arbitrary efficiency of the continuous monitoring. For the detection strategies considered, we show that: i) in the case of perfect continuous detection, the quantum Fisher information (QFI) of the conditional states is equal to the one obtained in the noiseless dynamics; ii) for smaller detection efficiencies, the QFI of the conditional state is equal to the QFI of a state undergoing the (unconditional) dephasing dynamics, but with an effectively reduced noise parameter.