Geometry of entanglement

Abstract

In the context of the surface-state correspondence we propose the geodesic curvature of a convex curve as a local measure of factorization of the dual Conformal Field Theory state. Its integral will be interpreted as computing the total bipartite entanglement among degrees of freedom with support on the chosen domain. We will derive results through application of the Gauss-Bonnet theorem and show quantitative agreement with computations using the Multiscale Entanglement Renormalization Ansatz tensor network and the formalism of entanglement density.