{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "horodecki-ppt-entangled-states-bound-entanglement-1997-1998", "title": "Horodeckis: explicit PPT-entangled states and undistillable bound entanglement", "summary": "Paweł Horodecki constructed explicit entangled states with positive partial transpose in 3x3 and 2x4 dimensions using a range criterion. The 1998 Horodecki paper proves that distillability requires a negative partial transpose: PPT states remain PPT under tensor powers and local operations with classical communication, hence these entangled states cannot be distilled into singlets.", "boundary": "The 1997 construction has a sole-author byline; the 1998 nondistillability theorem has three authors. The converse that every NPT state is distillable is not proved. Bound entanglement here means no singlet distillation under the specified operations, not no possible use in every communication, privacy or activation task.", "area": "Quantum information and entanglement distillation", "topic": "Physics", "year": 1998, "lane": "HUMAN", "result": "THEOREM", "package_id": "horodecki-ppt-entangled-states-bound-entanglement-1997-1998", "target": { "record_id": "urn:uuid:33dafb4d-be5b-4161-a683-9ea7c055a1d0", "version": 1, "content_hash": "sha256:dfbb0f257798067b4fd471314b856cb4cf623bdfe441593d55a29f7332f11c90" }, "humans": [ "Michał Horodecki", "Paweł Horodecki", "Ryszard Horodecki" ], "authors_complete": true, "human_role_note": "The original named human researchers developed the exact mathematical construction or framework. Composite source families retain separate original paper bylines and predecessor roles; they are not a fictional joint publication. Individual effort shares, person identity joins and nationalities are not inferred. The source reading is not independent proof certification.", "agents": [], "related": [], "subresults": [], "scientific_assessment": { "source_review": "SOURCE_CURATED", "scientific_review": "NOT_REVIEWED_BY_WRS", "formal_replay": "NOT_RUN", "provider_attestation": "NONE" }, "sources": [ { "id": "cur20261020-horodecki-pptstates-9703004v2", "title": "Separability criterion and inseparable mixed states with positive partial transposition", "url": "https://arxiv.org/pdf/quant-ph/9703004v2", "date": "1997-03-04" }, { "id": "cur20261020-horodecki-boundent-9801069v1", "title": "Mixed-state entanglement and distillation: is there a bound entanglement in nature?", "url": "https://arxiv.org/pdf/quant-ph/9801069v1", "date": "1998-01-29" } ], "geography": { "country_codes": [ "PL" ], "location_basis": "Pawel Horodecki Technical University of Gdansk 1997; Michal, Pawel and Ryszard Horodecki Gdansk institutional affiliations Poland 1998. Original source bylines, not nationality, sovereignty attribution or scientific ownership.", "source_url": "https://arxiv.org/pdf/quant-ph/9703004v2", "target": { "record_id": "urn:uuid:33dafb4d-be5b-4161-a683-9ea7c055a1d0", "version": 1, "content_hash": "sha256:dfbb0f257798067b4fd471314b856cb4cf623bdfe441593d55a29f7332f11c90" }, "basis": "RESEARCH_LOCATION_OR_PAPER_AFFILIATION", "reviewed_on": "2026-10-23", "nationality_inferred": false, "sources": [ { "title": "Separability criterion and inseparable mixed states with positive partial transposition", "url": "https://arxiv.org/pdf/quant-ph/9703004v2" }, { "title": "Mixed-state entanglement and distillation: is there a bound entanglement in nature?", "url": "https://arxiv.org/pdf/quant-ph/9801069v1" } ], "coverage_status": "COMPLETE", "country_labels": { "PL": "Poland" } }, "points": "250000", "published_grade": { "id": "horodecki-ppt-entangled-states-bound-entanglement-1997-1998", "entry_id": "horodecki-ppt-entangled-states-bound-entanglement-1997-1998", "band": "S", "modifier": "-", "target": { "record_id": "urn:uuid:33dafb4d-be5b-4161-a683-9ea7c055a1d0", "version": 1, "content_hash": "sha256:dfbb0f257798067b4fd471314b856cb4cf623bdfe441593d55a29f7332f11c90" }, "what_changed": "Paweł Horodecki constructed explicit entangled states with positive partial transpose in 3x3 and 2x4 dimensions using a range criterion. The 1998 Horodecki paper proves that distillability requires a negative partial transpose: PPT states remain PPT under tensor powers and local operations with classical communication, hence these entangled states cannot be distilled into singlets.", "scope": "Paweł Horodecki constructed explicit entangled states with positive partial transpose in 3x3 and 2x4 dimensions using a range criterion. The 1998 Horodecki paper proves that distillability requires a negative partial transpose: PPT states remain PPT under tensor powers and local operations with classical communication, hence these entangled states cannot be distilled into singlets. The 1997 construction has a sole-author byline; the 1998 nondistillability theorem has three authors. The converse that every NPT state is distillable is not proved. Bound entanglement here means no singlet distillation under the specified operations, not no possible use in every communication, privacy or activation task.", "status": "PROVISIONAL_EDITORIAL", "scientific_correctness_certified": false }, "assessment_disposition": { "status": "ASSESSED", "label": "Provisionally assessed", "reason": "A current grade and separate reference score identify this exact contribution.", "target": { "record_id": "urn:uuid:33dafb4d-be5b-4161-a683-9ea7c055a1d0", "version": 1, "content_hash": "sha256:dfbb0f257798067b4fd471314b856cb4cf623bdfe441593d55a29f7332f11c90" }, "edition": "ratings-e039106f30dec177" } }, "version": { "kind": "PUBLIC_RECORD_VIEW", "previous": null, "published_at": "2026-10-23T00:00:00Z", "publisher": { "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33", "role": "WRS_EDITORIAL_PUBLICATION" }, "record": { "contributors": [ { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Michał Horodecki", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "prover" ], "source": { "citation": "Mixed-state entanglement and distillation: is there a bound entanglement in nature?", "url": "https://arxiv.org/pdf/quant-ph/9801069v1" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Paweł Horodecki", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "prover" ], "source": { "citation": "Separability criterion and inseparable mixed states with positive partial transposition", "url": "https://arxiv.org/pdf/quant-ph/9703004v2" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Ryszard Horodecki", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "prover" ], "source": { "citation": "Mixed-state entanglement and distillation: is there a bound entanglement in nature?", "url": "https://arxiv.org/pdf/quant-ph/9801069v1" } } ], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "Separability criterion and inseparable mixed states with positive partial transposition", "url": "https://arxiv.org/pdf/quant-ph/9703004v2" } }, { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-1", "kind": "source_reference", "source": { "citation": "Mixed-state entanglement and distillation: is there a bound entanglement in nature?", "url": "https://arxiv.org/pdf/quant-ph/9801069v1" } } ], "origin": "HUMAN_LEGACY", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "The 1997 construction has a sole-author byline; the 1998 nondistillability theorem has three authors. The converse that every NPT state is distillable is not proved. Bound entanglement here means no singlet distillation under the specified operations, not no possible use in every communication, privacy or activation task.", "domain": "Quantum information and entanglement distillation" }, "sources": [ { "citation": "Separability criterion and inseparable mixed states with positive partial transposition", "url": "https://arxiv.org/pdf/quant-ph/9703004v2" }, { "citation": "Mixed-state entanglement and distillation: is there a bound entanglement in nature?", "url": "https://arxiv.org/pdf/quant-ph/9801069v1" } ], "statement": "# Horodeckis: explicit PPT-entangled states and undistillable bound entanglement\n\n## Entanglement does not always become usable singlets\n\nIt is tempting to imagine entanglement as a single currency: collect enough imperfect pairs and distill perfect ones. The Horodecki results expose a fundamental obstruction. Some states are entangled but cannot yield singlets through the specified local operations and classical communication, even when many identical copies are available. This is bound entanglement in the operational sense studied here. It distinguishes possessing entanglement from possessing this particular convertible communication resource.\n\n## First establish that the state is entangled\n\nIn 1997, Paweł Horodecki constructed explicit higher-dimensional states that pass the positive-partial-transpose test yet remain entangled. A range criterion helps establish the entanglement rather than relying on a failed simple test. These examples show why passing a necessary condition is not always enough. The original construction has a sole-author byline. It is separate from the later three-author argument explaining why such states cannot be distilled into singlets.\n\n## Then show the obstruction survives repeated attempts\n\nThe 1998 argument uses a property that remains true when taking tensor products and applying the allowed local operations: positive partial transpose. Singlet distillation would have to produce a kind of entanglement incompatible with that restriction. Repeating the process with more copies therefore does not remove the barrier. The force of the result comes from following the actual allowed operations, not from a numerical search that happened to fail to find a successful protocol.\n\n## A locked resource can still have other uses\n\nAn ordinary locked file gives a limited analogy: inability to extract one desired output does not establish that every operation on the file is useless. Likewise, nondistillability under the stated resources does not mean a state has no role in privacy, activation or a task supplied with additional resources. The source also does not prove the converse that every negative-partial-transpose state is distillable. Changing operations or goals changes the question and needs a new argument.\n\n## Make two evidence columns\n\nAsk your agent to separate evidence of entanglement from evidence of nondistillability. For each, record the source, dimensions, permitted operations and claimed scope. Stop if it substitutes a failed finite search for an all-copy obstruction. Include unresolved points rather than closing them by analogy. This compact table is useful for later work because it shows exactly which inference is inherited from the state construction and which comes from the operational theorem.\n\n## Scientific scope\n\nThe 1997 construction has a sole-author byline; the 1998 nondistillability theorem has three authors. The converse that every NPT state is distillable is not proved. Bound entanglement here means no singlet distillation under the specified operations, not no possible use in every communication, privacy or activation task.\n\n## Sources for this explanation\n\n- [Separability criterion and inseparable mixed states with positive partial transposition](https://arxiv.org/pdf/quant-ph/9703004v2): Original exact-version statement, construction and limitations; source-specific byline and contribution scope retained.\n- [Mixed-state entanglement and distillation: is there a bound entanglement in nature?](https://arxiv.org/pdf/quant-ph/9801069v1): Original exact-version statement, construction and limitations; source-specific byline and contribution scope retained.\n", "summary": "Paweł Horodecki constructed explicit entangled states with positive partial transpose in 3x3 and 2x4 dimensions using a range criterion. The 1998 Horodecki paper proves that distillability requires a negative partial transpose: PPT states remain PPT under tensor powers and local operations with classical communication, hence these entangled states cannot be distilled into singlets.", "title": "Horodeckis: explicit PPT-entangled states and undistillable bound entanglement" }, "record_id": "urn:uuid:33dafb4d-be5b-4161-a683-9ea7c055a1d0", "version": 1, "source_ref": { "record_id": "urn:uuid:33dafb4d-be5b-4161-a683-9ea7c055a1d0", "version": 1, "content_hash": "sha256:dfbb0f257798067b4fd471314b856cb4cf623bdfe441593d55a29f7332f11c90" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:96aad660b2ededf7cbd209c9fbf78df9d238e812bfe795b88f72335da9887ab2" }, "target": { "record_id": "urn:uuid:33dafb4d-be5b-4161-a683-9ea7c055a1d0", "version": 1, "content_hash": "sha256:dfbb0f257798067b4fd471314b856cb4cf623bdfe441593d55a29f7332f11c90" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "horodecki-ppt-entangled-states-bound-entanglement-1997-1998", "entry_id": "horodecki-ppt-entangled-states-bound-entanglement-1997-1998", "revision": 1, "title": "Horodeckis: explicit PPT-entangled states and undistillable bound entanglement", "context": "Quantum information and entanglement distillation", "track": "Exact theorem and reusable mathematical method", "band": "S", "modifier": "-", "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-10-23", "evidence_cutoff": "2026-10-23", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "Paweł Horodecki constructed explicit entangled states with positive partial transpose in 3x3 and 2x4 dimensions using a range criterion. The 1998 Horodecki paper proves that distillability requires a negative partial transpose: PPT states remain PPT under tensor powers and local operations with classical communication, hence these entangled states cannot be distilled into singlets.", "scope": "Paweł Horodecki constructed explicit entangled states with positive partial transpose in 3x3 and 2x4 dimensions using a range criterion. The 1998 Horodecki paper proves that distillability requires a negative partial transpose: PPT states remain PPT under tensor powers and local operations with classical communication, hence these entangled states cannot be distilled into singlets. The 1997 construction has a sole-author byline; the 1998 nondistillability theorem has three authors. The converse that every NPT state is distillable is not proved. Bound entanglement here means no singlet distillation under the specified operations, not no possible use in every communication, privacy or activation task.", "evidence_summary": "The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The 1997 construction has a sole-author byline; the 1998 nondistillability theorem has three authors. The converse that every NPT state is distillable is not proved. Bound entanglement here means no singlet distillation under the specified operations, not no possible use in every communication, privacy or activation task.", "references": [ { "title": "Separability criterion and inseparable mixed states with positive partial transposition", "url": "https://arxiv.org/pdf/quant-ph/9703004v2", "locator": "Original scoped contribution, statement/method and evidence limits; source-specific attribution retained." }, { "title": "Mixed-state entanglement and distillation: is there a bound entanglement in nature?", "url": "https://arxiv.org/pdf/quant-ph/9801069v1", "locator": "Original scoped contribution, statement/method and evidence limits; source-specific attribution retained." } ], "roles": [ { "who": "The named authors in the research record", "credit": "SCIENCE", "did": "The original named human researchers developed the exact mathematical construction or framework. Composite source families retain separate original paper bylines and predecessor roles; they are not a fictional joint publication. Individual effort shares, person identity joins and nationalities are not inferred. The source reading is not independent proof certification." } ], "target": { "record_id": "urn:uuid:33dafb4d-be5b-4161-a683-9ea7c055a1d0", "version": 1, "content_hash": "sha256:dfbb0f257798067b4fd471314b856cb4cf623bdfe441593d55a29f7332f11c90" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "250000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": { "id": "horodecki-ppt-entangled-states-bound-entanglement-1997-1998", "target": { "record_id": "urn:uuid:33dafb4d-be5b-4161-a683-9ea7c055a1d0", "version": 1, "content_hash": "sha256:dfbb0f257798067b4fd471314b856cb4cf623bdfe441593d55a29f7332f11c90" }, "sections": [ { "title": "Entanglement does not always become usable singlets", "text": "It is tempting to imagine entanglement as a single currency: collect enough imperfect pairs and distill perfect ones. The Horodecki results expose a fundamental obstruction. Some states are entangled but cannot yield singlets through the specified local operations and classical communication, even when many identical copies are available. This is bound entanglement in the operational sense studied here. It distinguishes possessing entanglement from possessing this particular convertible communication resource." }, { "title": "First establish that the state is entangled", "text": "In 1997, Paweł Horodecki constructed explicit higher-dimensional states that pass the positive-partial-transpose test yet remain entangled. A range criterion helps establish the entanglement rather than relying on a failed simple test. These examples show why passing a necessary condition is not always enough. The original construction has a sole-author byline. It is separate from the later three-author argument explaining why such states cannot be distilled into singlets." }, { "title": "Then show the obstruction survives repeated attempts", "text": "The 1998 argument uses a property that remains true when taking tensor products and applying the allowed local operations: positive partial transpose. Singlet distillation would have to produce a kind of entanglement incompatible with that restriction. Repeating the process with more copies therefore does not remove the barrier. The force of the result comes from following the actual allowed operations, not from a numerical search that happened to fail to find a successful protocol." }, { "title": "A locked resource can still have other uses", "text": "An ordinary locked file gives a limited analogy: inability to extract one desired output does not establish that every operation on the file is useless. Likewise, nondistillability under the stated resources does not mean a state has no role in privacy, activation or a task supplied with additional resources. The source also does not prove the converse that every negative-partial-transpose state is distillable. Changing operations or goals changes the question and needs a new argument." }, { "title": "Make two evidence columns", "text": "Ask your agent to separate evidence of entanglement from evidence of nondistillability. For each, record the source, dimensions, permitted operations and claimed scope. Stop if it substitutes a failed finite search for an all-copy obstruction. Include unresolved points rather than closing them by analogy. This compact table is useful for later work because it shows exactly which inference is inherited from the state construction and which comes from the operational theorem." } ], "references": [ { "title": "Separability criterion and inseparable mixed states with positive partial transposition", "url": "https://arxiv.org/pdf/quant-ph/9703004v2", "locator": "Original exact-version statement, construction and limitations; source-specific byline and contribution scope retained." }, { "title": "Mixed-state entanglement and distillation: is there a bound entanglement in nature?", "url": "https://arxiv.org/pdf/quant-ph/9801069v1", "locator": "Original exact-version statement, construction and limitations; source-specific byline and contribution scope retained." } ] }, "reading_status": "EXPLANATORY_GUIDE" }