A Geometric Area Bound for Information Transfer Through Semiclassical Traversable Wormholes

We prove a new area theorem in general relativity showing that, after a Gao-Jafferis-Wall deformation is switched off, the area of a wormhole throat cross-section cannot increase under infalling matter obeying the null energy condition. As a consequence, the minimal throat area sets a sharp upper bound on information transfer. Using the max-flow/min-cut formulation of bit threads, we show that the number of independent quantum degrees of freedom that can be transmitted through a semiclassical traversable wormhole is bounded by the throat area. We further illustrate the bound with a holographic tensor-network toy model built from two glued HaPPY codes.