Resolving spurious topological entanglement entropy in stabilizer codes

TL;DR

This paper addresses the issue of spurious contributions in topological entanglement entropy calculations for stabilizer codes, proposing a new partition method that eliminates these artifacts and exploring topological frustration effects.

Contribution

It introduces a concave partition method for stabilizer codes that rigorously removes spurious TEE contributions, improving the accuracy of topological order diagnostics.

Findings

The new partition method is proven to be free of spurious contributions.

Entanglement entropy in bicycle codes depends on cylinder circumference, indicating topological frustration.

Abstract

Topological entanglement entropy (TEE) is a key diagnostic of long-range entanglement in two-dimensional gapped phases of matter, but it can suffer from spurious contributions that overestimate the total quantum dimension of the underlying topological order. In this work, we identify the microscopic origin of spurious TEE and introduce a concave partition for computing the Levin-Wen TEE of translation-invariant stabilizer codes of prime-dimensional qudits. We rigorously prove that this prescription is free of spurious contributions. As a complementary probe, we study bivariate bicycle codes on a bipartite cylinder and show that the entanglement entropy depends sensitively on the cylinder circumference, revealing topological frustration of the underlying anyons.