Increasing the stability of the topological entanglement entropy

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.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.

quant-pharXiv:2604.27053May 1, 20260 citations

Bekenstein-Hawking entropy as topological entanglement entropy

Lauren McGough, Herman Verlinde

arXiv:1308.2342Journal of High Energy PhysicsNov 1, 201374 citations

Genuine Multi-Entropy in the Toric Code

Sriram Akella, Norihiro Iizuka, Akihiro Miyata

We study genuine multi-entropy as a diagnostic of multipartite entanglement in the toric code, which provides a controlled setting for probing multipartite structures in topologically ordered states. Our main question is whether genuine multi-entropy captures information that is not reducible to conventional lower-party entropic data, such as topological entanglement entropy. We first analyze toric-code ground states that admit a stabilizer-state description, where the relevant quantities can be evaluated exactly. We conjecture that, for stabilizer states and $\mathtt{q}\ge4$ , the $\mathtt{q}$ -partite genuine multi-entropy at replica index $n<\mathtt{q}$ collapses to a linear combination of multi-entropies involving at most $\mathtt{q}-2$ parties. We establish this pattern explicitly for $\mathtt{q}=4$ in the toric code stabilizer sector: for $n=2,3$ , the genuine multi-entropy is proportional to the tripartite information $I_3$ and, for the Kitaev-Preskill partition, contains no independent genuine four-partite information beyond that captured by the topological entanglement entropy. At $n=4$ , however, this reduction breaks down: the genuine multi-entropy is no longer proportional to $I_3$ , but remains a topological invariant of the toric-code stabilizer ground states under Kitaev-Preskill-preserving deformations that do not change whether the numbers of vertex- and plaquette-type junctions coincide. For generic non-stabilizer superpositions within the ground-state manifold and for coherent superpositions of local excitations, the low- $n$ reduction also fails. These results show that genuine multi-entropy probes multipartite entanglement structure beyond the tripartite information, and hence beyond the topological entanglement entropy in the Kitaev-Preskill partition, whereas for stabilizer states at low replica index it reduces to lower-partite entropic data.We study genuine multi-entropy as a diagnostic of multipartite entanglement in the toric code, which provides a controlled setting for probing multipartite structures in topologically ordered states. Our main question is whether genuine multi-entropy captures information that is not reducible to conventional lower-party entropic data, such as topological entanglement entropy. We first analyze toric-code ground states that admit a stabilizer-state description, where the relevant quantities can be evaluated exactly. We conjecture that, for stabilizer states and $\mathtt{q}\ge4$, the $\mathtt{q}$-partite genuine multi-entropy at replica index $n<\mathtt{q}$ collapses to a linear combination of multi-entropies involving at most $\mathtt{q}-2$ parties. We establish this pattern explicitly for $\mathtt{q}=4$ in the toric code stabilizer sector: for $n=2,3$, the genuine multi-entropy is proportional to the tripartite information $I_3$ and, for the Kitaev-Preskill partition, contains no independent genuine four-partite information beyond that captured by the topological entanglement entropy. At $n=4$, however, this reduction breaks down: the genuine multi-entropy is no longer proportional to $I_3$, but remains a topological invariant of the toric-code stabilizer ground states under Kitaev-Preskill-preserving deformations that do not change whether the numbers of vertex- and plaquette-type junctions coincide. For generic non-stabilizer superpositions within the ground-state manifold and for coherent superpositions of local excitations, the low-$n$ reduction also fails. These results show that genuine multi-entropy probes multipartite entanglement structure beyond the tripartite information, and hence beyond the topological entanglement entropy in the Kitaev-Preskill partition, whereas for stabilizer states at low replica index it reduces to lower-partite entropic data.

hep-thCross-listedarXiv:2607.06050Jul 8, 20260 citations

Topological entanglement entropy: an information-theoretic viewpoint

Bei Zeng

Jan 1, 20160 citations

Convergence of Topological Entanglement Entropy for Finite Size Systems

Clare I. Abreu, Raúl Herrera, Edward H. Rezayi

Bulletin of the American Physical SocietyMar 3, 20140 citations

Identifying topological order by entanglement entropy

Hong‐Chen Jiang, Zhenghan Wang, Leon Balents

arXiv:1205.4289Nature PhysicsNov 11, 2012633 citations

\mathtt{q}\ge4

, the

\mathtt{q}

-partite genuine multi-entropy at replica index

n<\mathtt{q}

collapses to a linear combination of multi-entropies involving at most

\mathtt{q}-2

parties. We establish this pattern explicitly for

\mathtt{q}=4

in the toric code stabilizer sector: for

n=2,3

, the genuine multi-entropy is proportional to the tripartite information

I_3

and, for the Kitaev-Preskill partition, contains no independent genuine four-partite information beyond that captured by the topological entanglement entropy. At

n=4

, however, this reduction breaks down: the genuine multi-entropy is no longer proportional to

I_3

, but remains a topological invariant of the toric-code stabilizer ground states under Kitaev-Preskill-preserving deformations that do not change whether the numbers of vertex- and plaquette-type junctions coincide. For generic non-stabilizer superpositions within the ground-state manifold and for coherent superpositions of local excitations, the low-

n

reduction also fails. These results show that genuine multi-entropy probes multipartite entanglement structure beyond the tripartite information, and hence beyond the topological entanglement entropy in the Kitaev-Preskill partition, whereas for stabilizer states at low replica index it reduces to lower-partite entropic data.