The three kinds of three-qubit entanglement

Szilárd Szalay

doi:10.22331/q-2026-10-22-2242

The three kinds of three-qubit entanglement

Szilárd Szalay

Department of Theoretical Solid State Physics, HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
Department of Theoretical Physics, University of the Basque Country UPV/EHU, Bilbao, Spain
EHU Quantum Center, University of the Basque Country UPV/EHU, Leioa, Biscay, Spain

Published:	2026-10-22, volume 10, page 2242
Editor:	Jens Siewert
Eprint:	arXiv:2511.07617v3
Doi:	https://doi.org/10.22331/q-2026-10-22-2242
Citation:	Quantum 10, 2242 (2026).

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Abstract

We construct an important missing piece in the entanglement theory of pure three-qubit states, which is a polynomial measure of W-entanglement. This works in parallel to the three-tangle, which is a polynomial measure of GHZ-entanglement, and to the bipartite concurrence, which is a polynomial measure of bipartite entanglement. We also show that these entanglement measures are ordered, the bipartite measure is larger than the W measure, which is larger than the GHZ measure. It is meaningful then to consider these three types of three-qubit entanglement, which are also ordered, bipartite is weaker than W, which is weaker than GHZ, in parallel to the order of the three kinds of equivalence classes of entangled three-qubit states.

Featured image: Illustration of the ordering of the measures of bipartite-, W- and GHZ-entanglement for the superposition of GHZ and W states.

► BibTeX data

@article{Szalay2026threekindsofthree,
  doi = {10.22331/q-2026-10-22-2242},
  url = {https://doi.org/10.22331/q-2026-10-22-2242},
  title = {The three kinds of three-qubit entanglement},
  author = {Szalay, Szil{\'{a}}rd},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2242},
  month = oct,
  year = {2026}
}

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