  In this paper, we find the boundary dual of the symplectic form for the bulk
fields in any entanglement wedge. The key ingredient is Uhlmann holonomy, which
is a notion of parallel transport of purifications of density matrices based on
a maximisation of transition probabilities. Using a replica trick, we compute
this holonomy for curves of reduced states in boundary subregions of
holographic QFTs at large N, subject to changes of operator insertions on the
boundary. It is shown that the Berry phase along Uhlmann parallel paths may be
written as the integral of an abelian connection whose curvature is the
symplectic form of the entanglement wedge. This generalises previous work on
holographic Berry curvature.
