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Peer-reviewedCC BY 4.0Quantum

The three kinds of three-qubit entanglement

  • Szilárd Szalay1,2,3
  1. 1Department of Theoretical Solid State Physics, HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
  2. 2Department of Theoretical Physics, University of the Basque Country UPV/EHU, Bilbao, Spain
  3. 3EHU Quantum Center, University of the Basque Country UPV/EHU, Leioa, Biscay, Spain
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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.

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Cite

BibTeXRIS
BibTeX
@article{szalay2026three,
  title = {{The three kinds of three-qubit entanglement}},
  author = {Szilárd Szalay},
  journal = {Quantum},
  year = {2026},
  month = oct,
  doi = {10.22331/q-2026-10-22-2242},
  url = {https://quantum-journal.org/papers/q-2026-10-22-2242/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - The three kinds of three-qubit entanglement
AU  - Szilárd Szalay
PY  - 2026
DA  - 2026/10/22
JO  - Quantum
DO  - 10.22331/q-2026-10-22-2242
UR  - https://quantum-journal.org/papers/q-2026-10-22-2242/
AB  - 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.
SN  - 2521-327X
ER  -