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PreprintarXiv licencearXiv

Separability from Multipartite Measures

  • Chen-Te Ma
  • Ma-Ke Yuan
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Abstract

We show that multi-invariants provide necessary and sufficient criteria for full separability in finite-dimensional multipartite systems. For tripartite three-qubit states, the third-order negativity gives an exact criterion for full separability for both pure and mixed states. We then extend the framework to four-qubit pure states, whose full characterization requires eighteen independent real parameters. We identify eighteen independent entanglement measures, consisting of six bipartite, eight tripartite, and four quadripartite measures, with the third-order negativity serving as a key separability criterion. Finally, we generalize the construction to multipartite qudit systems and discuss an application to conformal field theory.

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Cite

BibTeXRIS
BibTeX
@misc{ma2026separability,
  title = {{Separability from Multipartite Measures}},
  author = {Chen-Te Ma and Ma-Ke Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.02097},
  eprint = {2605.02097},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.02097},
}
RIS
TY  - UNPB
TI  - Separability from Multipartite Measures
AU  - Chen-Te Ma
AU  - Ma-Ke Yuan
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2605.02097
UR  - https://arxiv.org/abs/2605.02097
AB  - We show that multi-invariants provide necessary and sufficient criteria for full separability in finite-dimensional multipartite systems. For tripartite three-qubit states, the third-order negativity gives an exact criterion for full separability for both pure and mixed states. We then extend the framework to four-qubit pure states, whose full characterization requires eighteen independent real parameters. We identify eighteen independent entanglement measures, consisting of six bipartite, eight tripartite, and four quadripartite measures, with the third-order negativity serving as a key separability criterion. Finally, we generalize the construction to multipartite qudit systems and discuss an application to conformal field theory.
ER  -