# Quantum coherence and state conversion: theory and experiment

## TL;DR

This paper provides a complete theoretical solution for optimal qubit state conversion probabilities in quantum coherence resource theory, extends the analysis to assisted scenarios with correlations, and experimentally demonstrates these optimal conversions using linear optics.

## Contribution

It offers the first complete solution for mixed state conversion probabilities in qubit coherence resource theory and experimentally verifies these optimal processes.

## Key findings

- Optimal probabilities for mixed state conversions determined
- Assisted incoherent state conversion enhances process efficiency
- Experimental demonstration of optimal conversions in linear optics

## Abstract

The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion of the resource. Here we solve this question completely for qubit states by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. Extending the discussion to distributed scenarios, we introduce and address the task of assisted incoherent state conversion where the process is enhanced by making use of correlations with a second party. Building on these results, we demonstrate experimentally that the optimal state conversion probabilities can be achieved in a linear optics set-up. This paves the way towards real world applications of coherence transformations in current quantum technologies.