# Characterisation of multi-level quantum coherence without ideal measurements

## TL;DR

This paper introduces a method to reliably quantify quantum coherence from interference patterns without requiring ideal measurements, ensuring accurate detection despite experimental imperfections.

## Contribution

It presents a new coherence certifier based on statistical interference properties that prevents overestimation of quantum superpositions under imperfect conditions.

## Key findings

- The certifier is robust against measurement imperfections.
- It prevents overestimating coherence from interference data.
- Numerical tests confirm resilience to state and measurement errors.

## Abstract

Coherent superpositions are one of the hallmarks of quantum mechanics and are vital for any quantum mechanical device to outperform the classically achievable. Generically, superpositions are verified in interference experiments, but despite their longstanding central role we know very little about how to extract the number of coherently superposed amplitudes from a general interference pattern. A fundamental issue is that performing a phase-sensitive measurement is as challenging as creating a coherent superposition, so that assuming a perfectly implemented measurement for verification of quantum coherence is hard to justify. In order to overcome this issue, we construct a coherence certifier derived from simple statistical properties of an interference pattern, such that any imperfection in the measurement can never over-estimate the number of coherently superposed amplitudes. We numerically test how robust this measure is to under-estimating the coherence in the case of imperfect state preparation or measurement, and find it to be very resilient in both cases.