Quantum Max-flow in the Bridge Graph

The quantum max-flow is a linear algebraic version of the classical max-flow of a graph, used in quantum many-body physics to quantify the maximal possible entanglement between two regions of a tensor network state. 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 spaces and the representation theory of quivers. Further, we highlight relations to invariant theory and to algebraic statistics.