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PreprintCC BY 4.0arXiv

Multi-entropy in random tensor networks

  • Miao Hu
  • Simon Lin
  • Ion Nechita
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Abstract

We study the evaluation of Rényi multi-entropies S(q)n in Random Tensor Network (RTN) states in the large bond-dimension limit. For the case of Rényi index n=2 and arbitrary number of parties q, we prove that that multi-entropies are determined by minimal multiway cuts through the network. When the minimal multiway cut is degenerate, we characterize the full minimizer set via compatible families of minimal cuts and give a criterion for all minimizers to come from ordinary cut partitions. For n=2, this gives a natural generalization of the minimal cut description of bipartite entanglement to multipartite systems with arbitrarily many parties. For the case of integer n>2, we show that the minimal multiway cut conjecture is in general \emph{not true} by providing explicit counter examples for both the single random tensor and for the network built from isometric tilings. We discuss the implication for our results on the multipartite entanglement structures in RTN and holography.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026multientropy,
  title = {{Multi-entropy in random tensor networks}},
  author = {Miao Hu and Simon Lin and Ion Nechita},
  howpublished = {arXiv},
  year = {2026},
  month = jun,
  doi = {10.48550/arxiv.2606.04470},
  eprint = {2606.04470},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.04470},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Multi-entropy in random tensor networks
AU  - Miao Hu
AU  - Simon Lin
AU  - Ion Nechita
PY  - 2026
DA  - 2026/06/12
PB  - arXiv
DO  - 10.48550/arxiv.2606.04470
UR  - https://arxiv.org/abs/2606.04470
AB  - We study the evaluation of Rényi multi-entropies S^(q)_n in Random Tensor Network (RTN) states in the large bond-dimension limit. For the case of Rényi index n=2 and arbitrary number of parties q, we prove that that multi-entropies are determined by minimal multiway cuts through the network. When the minimal multiway cut is degenerate, we characterize the full minimizer set via compatible families of minimal cuts and give a criterion for all minimizers to come from ordinary cut partitions. For n=2, this gives a natural generalization of the minimal cut description of bipartite entanglement to multipartite systems with arbitrarily many parties. For the case of integer n>2, we show that the minimal multiway cut conjecture is in general \emph{not true} by providing explicit counter examples for both the single random tensor and for the network built from isometric tilings. We discuss the implication for our results on the multipartite entanglement structures in RTN and holography.
ER  -