{
  "abstract": "In this work, we show that a two-qubit entangled state admitting at least one pure steered state is Einstein-Podolsky-Rosen (EPR) steerable from Alice to Bob. Pure steered states signifies that the quantum steering ellipsoid of Bob is tangent to his Bloch sphere at least at a single point. Furthermore, we prove that for a two-qubit entangled state, Bob's quantum steering ellipsoid is tangent to his Bloch sphere at exactly $N$ points, for $N\\in \\{ 0,1,2,\\infty\\}$, if and only if Alice's quantum steering ellipsoid is tangent to her Bloch sphere at exactly $N$ points. For any two-qubit entangled state, therefore, if one party can steer the other to at least one pure state, the state is two-way EPR steerable. We also present several illuminating examples of two-qubit entangled states such that the EPR steering can be verified in terms of pure steered states. Our result addresses the Gisin theorem in a EPR steering scenario: at least a single pure steered state implies two-way steering.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.18243",
  "author_total": 2,
  "authors": [
    {
      "name": "Qiu-Cheng Song"
    },
    {
      "name": "Joonwoo Bae"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3y9d9pvf4xqfz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.18243",
  "fulltext_url": null,
  "id": "3y9d9pvf4xqfz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.18243",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7161727246",
  "pdf_url": "https://arxiv.org/pdf/2605.18243",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3y9d9pvf4xqfz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2605.18243",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.18243"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "One pure steered state implies Einstein-Podolsky-Rosen steering for two-qubit entangled states",
  "title_text": "One pure steered state implies Einstein-Podolsky-Rosen steering for two-qubit entangled states",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/3y9d9pvf4xqfz",
  "venue": "arXiv",
  "versions": []
}