Optimized parameter estimation in the presence of collective phase noise

TL;DR

This paper explores advanced measurement strategies for phase and frequency estimation under collective phase noise, demonstrating optimized probe states and differential interferometry to achieve near-Heisenberg sensitivity.

Contribution

It introduces experimentally feasible optimization of initial states and shows that differential interferometry with GHZ and Dicke states can reach sub-shot noise sensitivity under collective phase noise.

Findings

Optimal rotation angles depend on measurement times.

Differential interferometry achieves near-Heisenberg sensitivity.

Symmetric Dicke states are effective for noise monitoring.

Abstract

We investigate phase and frequency estimation with different measurement strategies under the effect of collective phase noise. First, we consider the standard linear estimation scheme and present an experimentally realisable optimization of the initial probe states by collective rotations. We identify the optimal rotation angle for different measurement times. Second, we show that sub-shot noise sensitivity - up to the Heisenberg limit - can be reached in presence of collective phase noise by using differential interferometry, where one part of the system is used to monitor the noise. For this, not only GHZ states but also symmetric Dicke states are suitable. We investigate the optimal splitting for a general symmetric Dicke state at both inputs and discuss possible experimental realisations of differential interferometry.