Quantum max-flow in the bridge graph

TL;DR

This paper computes the quantum max-flow exactly for the bridge graph, linking tensor network entanglement measures to advanced algebraic and representation theories, and highlighting their broader mathematical connections.

Contribution

It provides an exact calculation of quantum max-flow for the bridge graph, introducing novel links to tensor theory, quiver representations, and invariant theory.

Findings

Exact quantum max-flow for the bridge graph derived.

Connections established between quantum max-flow, tensor theory, and algebraic structures.

Highlights relations to invariant theory and algebraic statistics.

Abstract

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.