  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.
