# Optimal entangled coherent states in lossy quantum-enhanced metrology

## TL;DR

This paper explores how to optimize entangled coherent states for quantum phase estimation in lossy interferometers, demonstrating that less entanglement can be more advantageous under higher losses to maintain quantum advantage.

## Contribution

It introduces a method to determine the optimal entangled coherent state configuration that maximizes quantum Fisher information under loss conditions, highlighting robustness and measurement strategies.

## Key findings

- Optimal state configuration decreases entanglement with increased loss
- Entangled coherent states outperform separable states in high-loss scenarios
- Correlation measurements are essential for optimal information extraction

## Abstract

We investigate an optimal distance of two components in an entangled coherent state for quantum phase estimation in lossy interferometry. The optimal distance is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Maximizing the formula of the quantum Fisher information over an input mean photon number, we show that, as the losses of the interferometer increase, it can be more beneficial to prepare an initially entangled coherent state that is less entangled. This represents that the optimal distance of the two-mode components decreases with more loss in the interferometry. Under the constraint of the input mean photon number, we obtain that the optimal entangled coherent state is more robust than a separable coherent state, even in a high photon loss rate. The optimal entangled coherent state preserves quantum advantage over the standard interferometric limit of the separable coherent state. We also show that the corresponding optimal measurement requires correlation measurement bases.