Seeing topological entanglement through the information convex

TL;DR

This paper uses the information convex framework to derive the topological entanglement entropy contribution from anyons and boundaries, linking it to quantum dimensions and fusion properties in topological orders.

Contribution

It provides a derivation of the topological entropy contribution using the information convex, connecting it to quantum dimensions and fusion constraints.

Findings

Derived the topological entropy contribution $\

Identified fusion probabilities and constraints on fusion theory.

Bound the circuit depth for non-Abelian string operators.

Abstract

The information convex allows us to look into certain information-theoretic constraints in two-dimensional topological orders. We provide a derivation of the topological contribution $\ln d_a$ to the von Neumann entropy, where $d_a$ is the quantum dimension of anyon $a$. This value emerges as the only value consistent with strong subadditivity, assuming a certain topological dependence of the information convex structure. In particular, it is assumed that the fusion multiplicities are coherently encoded in a 2-hole disk. A similar contribution ($\ln d_{\alpha}$) is derived for gapped boundaries. This method further allows us to identify the fusion probabilities and certain constraints on the fusion theory. We also derive a linear bound on the circuit depth of unitary non-Abelian string operators and discuss how it generalizes and changes in the presence of a gapped boundary.