Coordinately assisted distillation of quantum coherence in multipartite system

We investigate the issue of assisted coherence distillation in the asymptotic limit, by coordinately performing the identical local operations on the auxiliary systems of each copy. When we further restrict the coordinate operations to projective measurements, the distillation process branches into many sub-processes. Finally, a computable measure of the assisted distillable coherence is derived as the maximal average coherence of the residual states with the maximization taken over all the projective measurements on the auxiliary. The measure can be conveniently used to evaluate the assisted distillable coherence in experiments, especially suitable for the case that the system and its auxiliary are in mixed states. By using the measure, we for the first time study the assisted coherence distillation in multipartite systems. Monogamy-like inequalities are derived to constrain the distribution of the assisted distillable coherence in the subsystems. Taking a three-qubit system for example, we experimentally prepare two types of tripartite correlated states, i.e., the W -type and GHZ-type states in a linear optical setup, and experimentally test the assisted distillable coherence. Theoretical and experimental results agree well to verify the distribution inequalities given by us. Three measures of multipartite quantum correlation are also considered. The close relationship between the assisted coherence distillation and the multipartite correlation is revealed.