Multipartite entanglement spreads
Abstract
The entanglement structure of a bipartite pure state is characterized by its entanglement spectrum, or equivalently, by the family of Rényi-k entanglement entropies with integer k. Taking the difference of two such entropies defines a quantity known as an entanglement spread, that is monotonous under local operations, and that vanishes if and only if the entanglement spectrum of the state is flat. We introduce a multipartite generalization of this notion which, for a fixed number D≥ 3 of parties, results in a collection of maps indexed by pairs of D-edge-colored graphs (obeying some condition). Each member of this collection takes the form of a difference of two multipartite Rényi entanglement entropies, each associated to a local unitary polynomial invariant (known in this context as a trace-invariant), and is shown to be monotonous under local operations. We then argue that a previously introduced family of so-called hypergraph-tensor (HT) states can be understood as a multipartite counterpart to the family of flat bipartite states. Indeed, we first prove that, when D=3, a tripartite pure state is HT if and only if it minimizes a particular (infinite) family of entanglement spreads. Second, we embed the set of HT states into the much larger family of spectral hypergraph-tensor (SHT) states, defined by a new Ansatz we introduce. We then prove that HT states can be uniquely characterized as the minimizers of some fixed entanglement spread among SHT states, for arbitrary D≥ 3. We also investigate SHT states in their own right: in particular, we characterize their orbits under local unitary transformations. Finally, along the way, the asymptotic large-N expectation values of a number of entanglement spreads are computed in the Haar-random state of local dimension N.
Related
BibTeX
@misc{carrozza2026multipartite,
title = {{Multipartite entanglement spreads}},
author = {Sylvain Carrozza and Johann Chevrier and Luca Lionni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12271},
eprint = {2610.12271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12271},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Multipartite entanglement spreads
AU - Sylvain Carrozza
AU - Johann Chevrier
AU - Luca Lionni
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12271
UR - https://arxiv.org/abs/2610.12271
AB - The entanglement structure of a bipartite pure state is characterized by its entanglement spectrum, or equivalently, by the family of Rényi-k entanglement entropies with integer k. Taking the difference of two such entropies defines a quantity known as an entanglement spread, that is monotonous under local operations, and that vanishes if and only if the entanglement spectrum of the state is flat. We introduce a multipartite generalization of this notion which, for a fixed number D≥ 3 of parties, results in a collection of maps indexed by pairs of D-edge-colored graphs (obeying some condition). Each member of this collection takes the form of a difference of two multipartite Rényi entanglement entropies, each associated to a local unitary polynomial invariant (known in this context as a trace-invariant), and is shown to be monotonous under local operations. We then argue that a previously introduced family of so-called hypergraph-tensor (HT) states can be understood as a multipartite counterpart to the family of flat bipartite states. Indeed, we first prove that, when D=3, a tripartite pure state is HT if and only if it minimizes a particular (infinite) family of entanglement spreads. Second, we embed the set of HT states into the much larger family of spectral hypergraph-tensor (SHT) states, defined by a new Ansatz we introduce. We then prove that HT states can be uniquely characterized as the minimizers of some fixed entanglement spread among SHT states, for arbitrary D≥ 3. We also investigate SHT states in their own right: in particular, we characterize their orbits under local unitary transformations. Finally, along the way, the asymptotic large-N expectation values of a number of entanglement spreads are computed in the Haar-random state of local dimension N.
ER -