# Measuring coherence of quantum measurements

## TL;DR

This paper introduces a method to quantify and verify the quantum coherence of measurements, demonstrating that certain photonic qubit measurements violate classical assumptions and are inherently quantum.

## Contribution

It develops an operational criterion to assess measurement-based quantum coherence, distinguishing quantum measurements from classical models.

## Key findings

- Polarization measurements of a single photonic qubit violate classical constraints.
- The method quantifies the quantum resourcefulness of measurements.
- Demonstrates the fundamental difference between quantum and classical measurement statistics.

## Abstract

The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on the implementation of its complementary concept, coherence from quantum measurements. By devising an accessible criterion which holds true in any classical statistical theory, we demonstrate that noncommutative quantum measurements violate this constraint, rendering it possible to perform an operational assessment of the measurement-based quantum coherence. In particular, we verify that polarization measurements of a single photonic qubit, an essential carrier of one unit of quantum information, are already incompatible with classical, i.e., incoherent, models of a measurement apparatus. Thus, we realize a method that enables us to quantitatively certify which quantum measurements follow fundamentally different statistical laws than expected from classical theories and, at the same time, quantify their usefulness within the modern framework of resources for quantum information technology.