# Quantum interferometry in multi-mode systems

## TL;DR

This paper explores how multi-mode structures in quantum interferometry affect phase estimation, revealing the relationship between particle entanglement and surpassing shot-noise limits, with implications for entanglement detection methods.

## Contribution

It generalizes the relation between entanglement and phase sensitivity to multi-mode systems, highlighting limitations of existing entanglement detection techniques in such contexts.

## Key findings

- Particle entanglement enables surpassing shot-noise limit in multi-mode interferometry.
- Existing entanglement detection methods can be misleading in multi-mode scenarios.
- Results apply to pure/mixed states with fixed or fluctuating particle numbers.

## Abstract

We consider the situation when the signal propagating through each arm of an interferometer has a complicated multi-mode structure. We find the relation between the particle-entanglement and the possibility to surpass the shot-noise limit of the phase estimation. Our results are general---they apply to pure and mixed states of identical and distinguishable particles (or combinations of both), for a fixed and fluctuating number of particles. We also show that the method for detecting the entanglement often used in two-mode system can give misleading results when applied to the multi-mode case.