# Theory-Independent Measure of Coherence

## TL;DR

This paper introduces a theory-independent framework for quantifying coherence, applicable to quantum and non-local models, using sequential measurement statistics to distinguish quantum coherence from other phenomena.

## Contribution

It proposes a novel, theory-independent method to measure coherence through measurement outcome deviations, applicable to quantum mechanics and non-local models.

## Key findings

- Introduces two new quantum coherence measures.
- Identifies a finite gap in coherence between non-local models and quantum mechanics.
- Provides a framework to distinguish quantum coherence from non-locality.

## Abstract

We provide a theory independent framework to quantify coherence. In comparison with Bell's theory independent approach to quantum nonlocality, we characterize a general coherence phenomenon with statistics arising from sequential measurements of observables that might not be compatible. By introducing a "decohered" state after the sharp measurement of some preferred observable, we quantify coherence by either the difference of initial "superposed" state from the "decohered" state or the measurement outcome deviations when they subjected to further measurements. Applied to quantum mechanics, the outcome-difference measures yield two novel quantum coherence measures, one of which upper-bounds quantum interference visibility. In the Bell's scenario, we find a finite gap of coherences between a super non-local model and quantum mechanic and therefore our framework can help to single out quantum mechanics beyond non-locality.