Universal lower bound on topological entanglement entropy

TL;DR

This paper proves that the topological entanglement entropy (TEE) has a universal lower bound, ensuring the predicted value from anyon theory is always less than or equal to the actual TEE, and introduces a circuit-invariant TEE definition.

Contribution

It establishes a nonnegativity property of the spurious TEE and defines a TEE measure invariant under constant-depth quantum circuits.

Findings

Spurious TEE is always nonnegative.

The predicted TEE from anyon theory is a universal lower bound.

Introduces a circuit-invariant TEE definition.

Abstract

Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE). In many models, the TEE takes a universal value that characterizes the underlying topological phase. However, the TEE is not truly universal: it can differ even for two states related by constant-depth circuits, which are necessarily in the same phase. The difference between the TEE and the value predicted by the anyon theory is often called the spurious topological entanglement entropy. We show that this spurious contribution is always nonnegative, thus the value predicted by the anyon theory provides a universal lower bound. This observation also leads to a definition of TEE that is invariant under constant-depth quantum circuits.