  We introduce a quantum notion of parallel transport between subsystems of a
quantum state whose holonomies characterize the structure of entanglement. In
AdS/CFT, entanglement holonomies are reflected in the bulk spacetime
connection. When the subsystems are a pair of holographic CFTs in an entangled
state, our quantum transport measures Wilson lines threading the dual wormhole.
For subregions of a single CFT it is generated by the modular Berry connection
and computes the effect of the AdS curvature on the transport of minimal
surfaces. Our observation reveals a new aspect of the spacetime-entanglement
duality and yet another concept shared between gravity and quantum mechanics.
