  The quantum max-flow quantifies the maximal possible entanglement between two
regions of a tensor network state for a fixed graph and fixed bond dimensions.
In this work, we calculate the quantum max-flow exactly in the case of the
bridge graph. The result is achieved by drawing connections to the theory of
prehomogenous tensor and the representation theory of quivers. Further, we
highlight relations to invariant theory and to algebraic statistics.
