dorsal/arxiv
View SchemaExistence Criterion of Genuine Tripartite Entanglement
| Authors | Chang-shui Yu He-shan Song |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603035 |
| URL | https://arxiv.org/abs/quant-ph/0603035 |
Abstract
In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits (Phys. Rev. A \textbf{61}, 052306 (2000)) to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states (Phys. Rev. A \textbf{72}, 022333 (2005)). A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and consider the existence of genuine tripartite entanglement of some weakly mixed states.
{
"annotation_id": "5ea5cc5a-184b-4bde-b61a-9e08fe9b3423",
"date_created": "2026-03-02T18:02:23.667000Z",
"date_modified": "2026-03-02T18:02:23.667000Z",
"file_hash": "41f11b0149ab2387e5fbc36fe678643d05b289413bcaa67ae6ddbeba6ad7dd7f",
"private": false,
"record": {
"abstract": "In this paper, an intuitive mathematical formulation is provided to\ngeneralize the residual entanglement for tripartite systems of qubits (Phys.\nRev. A \\textbf{61}, 052306 (2000)) to the tripartite systems in higher\ndimension. The spirit lies in the tensor treatment of tripartite pure states\n(Phys. Rev. A \\textbf{72}, 022333 (2005)). A distinct characteristic of the\npresent generalization is that the formulation for higher dimensional systems\nis invariant under permutation of the subsystems, hence is employed as a\ncriterion to test the existence of genuine tripartite entanglement.\nFurthermore, the formulation for pure states can be conveniently extended to\nthe case of mixed states by utilizing the kronecker product approximate\ntechnique. As applications, we give the analytic approximation of the criterion\nfor weakly mixed tripartite quantum states and consider the existence of\ngenuine tripartite entanglement of some weakly mixed states.",
"arxiv_id": "quant-ph/0603035",
"authors": [
"Chang-shui Yu He-shan Song"
],
"categories": [
"quant-ph"
],
"title": "Existence Criterion of Genuine Tripartite Entanglement",
"url": "https://arxiv.org/abs/quant-ph/0603035"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "966beb3d-de31-4015-bc89-1146b4e63939",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}