Unraveling quantum phase estimation: exploring the impact of multi-photon interference on the quantum Fisher information

TL;DR

This paper investigates how multi-photon interference affects quantum Fisher information and phase estimation precision, revealing that partially distinguishable multi-photon states can outperform traditional two-photon setups in quantum metrology.

Contribution

It provides a comprehensive theoretical and experimental analysis of four-photon interference and its impact on quantum Fisher information for phase estimation.

Findings

Partially distinguishable multi-photon states can yield higher Fisher information than two-photon states.

Multi-photon interference patterns are non-monotonic with respect to distinguishability.

Tools are developed to quantify multi-photon interference effects on measurement precision.

Abstract

Quantum interference is known to become extinct with distinguishing information, as illustrated by the ubiquitous double-slit experiment or the two-photon HOM effect. In the former case single particle interference is destroyed with which-path information while in the latter bunching interference tails-off as photons become distinguishable. It has been observed that when more than two particles are involved, these interference patterns are in general a non monotonic function of the distinguishability. Here we perform a comprehensive characterization, both theoretically and experimentally, of four-photon interference by analyzing the corresponding correlation functions, contemplating several degrees of distinguishability across different parameters. This study provides all the necessary tools to quantify the impact of multi-photon interference on precision measurements of parameters such as phase, frequency, and time difference. We apply these insights to quantify the precision in the estimation of an interferometric phase in a two-port interferometer using a four-photon state. Our results reveal that, for certain phase values, partially distinguishable multi-photon states can achieve higher Fisher information values compared to the two-photon experiment. These findings highlight the potential of distinguishable multi-photon states for enhanced precision in quantum metrology and related applications.