{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "bennett-et-al-noisy-entanglement-purification-1995", "title": "Bennett et al.: distilling noisy entanglement for faithful teleportation", "summary": "Local operations coordinated by classical messages can distill fewer high-quality entangled pairs from many imperfect two-qubit pairs whose singlet fidelity exceeds one half. The work introduces two-way recurrence purification and seeded asymptotic breeding, providing entanglement that can support faithful teleportation across a noisy link.", "boundary": "Fidelity above one half is sufficient for this two-qubit protocol, not a complete higher-dimensional distillability criterion. Fixed-block recurrence alone has vanishing yield in the perfect-output limit; the positive-rate construction adds variable blocks and breeding resources. The later unseeded one-way hashing protocol is a separate contribution. Ideal local operations and classical messages are assumed; optimal yield is not determined.", "area": "Quantum communication and entanglement", "topic": "Physics", "year": 1995, "lane": "HUMAN", "result": "THEOREM", "package_id": "bennett-et-al-noisy-entanglement-purification-1995", "target": { "record_id": "urn:uuid:ade3abcf-69d2-4201-ae91-9ffae23f549b", "version": 1, "content_hash": "sha256:7a5c7e7c4d2387940a0a960a76ebea5f77a1d6b355c6aa87eb344162f8bc9bdc" }, "humans": [ "Charles H. Bennett", "Gilles Brassard", "Sandu Popescu", "Benjamin Schumacher", "John A. Smolin", "William K. Wootters" ], "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-arxiv-quant-ph-9511027v2", "title": "Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels", "url": "https://arxiv.org/abs/quant-ph/9511027v2", "date": "1995-11-22" } ], "geography": { "country_codes": [ "US", "CA", "IL" ], "location_basis": "Bennett IBM NY, Brassard Universite de Montreal Canada, Popescu Tel Aviv Israel, Schumacher Kenyon Ohio, Smolin UCLA and Wootters Williams Massachusetts US. Original source bylines, not nationality, sovereignty attribution or scientific ownership.", "source_url": "https://arxiv.org/abs/quant-ph/9511027v2", "target": { "record_id": "urn:uuid:ade3abcf-69d2-4201-ae91-9ffae23f549b", "version": 1, "content_hash": "sha256:7a5c7e7c4d2387940a0a960a76ebea5f77a1d6b355c6aa87eb344162f8bc9bdc" }, "basis": "RESEARCH_LOCATION_OR_PAPER_AFFILIATION", "reviewed_on": "2026-10-23", "nationality_inferred": false, "sources": [ { "title": "Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels", "url": "https://arxiv.org/abs/quant-ph/9511027v2" } ], "coverage_status": "COMPLETE", "country_labels": { "US": "United States", "CA": "Canada", "IL": "Israel" } }, "points": "150000", "published_grade": { "id": "bennett-et-al-noisy-entanglement-purification-1995", "entry_id": "bennett-et-al-noisy-entanglement-purification-1995", "band": "A", "modifier": "+", "target": { "record_id": "urn:uuid:ade3abcf-69d2-4201-ae91-9ffae23f549b", "version": 1, "content_hash": "sha256:7a5c7e7c4d2387940a0a960a76ebea5f77a1d6b355c6aa87eb344162f8bc9bdc" }, "what_changed": "Local operations coordinated by classical messages can distill fewer high-quality entangled pairs from many imperfect two-qubit pairs whose singlet fidelity exceeds one half. The work introduces two-way recurrence purification and seeded asymptotic breeding, providing entanglement that can support faithful teleportation across a noisy link.", "scope": "Local operations coordinated by classical messages can distill fewer high-quality entangled pairs from many imperfect two-qubit pairs whose singlet fidelity exceeds one half. The work introduces two-way recurrence purification and seeded asymptotic breeding, providing entanglement that can support faithful teleportation across a noisy link. Fidelity above one half is sufficient for this two-qubit protocol, not a complete higher-dimensional distillability criterion. Fixed-block recurrence alone has vanishing yield in the perfect-output limit; the positive-rate construction adds variable blocks and breeding resources. The later unseeded one-way hashing protocol is a separate contribution. Ideal local operations and classical messages are assumed; optimal yield is not determined.", "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:ade3abcf-69d2-4201-ae91-9ffae23f549b", "version": 1, "content_hash": "sha256:7a5c7e7c4d2387940a0a960a76ebea5f77a1d6b355c6aa87eb344162f8bc9bdc" }, "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": "Charles H. 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Smolin", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "prover" ], "source": { "citation": "Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels", "url": "https://arxiv.org/abs/quant-ph/9511027v2" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "William K. Wootters", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "prover" ], "source": { "citation": "Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels", "url": "https://arxiv.org/abs/quant-ph/9511027v2" } } ], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels", "url": "https://arxiv.org/abs/quant-ph/9511027v2" } } ], "origin": "HUMAN_LEGACY", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "Fidelity above one half is sufficient for this two-qubit protocol, not a complete higher-dimensional distillability criterion. Fixed-block recurrence alone has vanishing yield in the perfect-output limit; the positive-rate construction adds variable blocks and breeding resources. The later unseeded one-way hashing protocol is a separate contribution. Ideal local operations and classical messages are assumed; optimal yield is not determined.", "domain": "Quantum communication and entanglement" }, "sources": [ { "citation": "Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels", "url": "https://arxiv.org/abs/quant-ph/9511027v2" } ], "statement": "# Bennett et al.: distilling noisy entanglement for faithful teleportation\n\n## Can noisy entanglement be cleaned?\n\nImagine two laboratories sharing many imperfect quantum pairs. A perfect pair could support teleportation, but noise has weakened the shared resource. Bennett and colleagues showed how the laboratories can sacrifice some pairs to improve others using local operations and ordinary classical messages. They do not send an unknown quantum state through the classical messages. The existing entanglement remains essential, and teleportation itself comes from earlier work rather than being invented again in this purification protocol.\n\n## Keep some pairs and discard others\n\nThe recurrence procedure combines two pairs, measures selected particles and compares the outcomes. Depending on those outcomes, the laboratories keep a surviving pair or discard it. The selected population can have higher singlet fidelity, meaning greater overlap with a chosen ideal entangled state. This is selection with a resource cost, not a way to improve every individual pair for free. Communicating the comparison results is part of the procedure.\n\n## Quality and quantity are separate numbers\n\nFor an invented input with singlet fidelity 0.8 in the paper's symmetric two-qubit family, the recurrence expression gives a kept-pair fidelity of about 0.838. That is an increase in quality, conditional on the stated protocol and selection. It does not mean 83.8 percent of the original pairs survive. Two input pairs are consumed in each trial, and some trials are rejected. Fidelity, acceptance probability and final yield answer different questions.\n\n## Why one improved pair is not the whole theorem\n\nRepeating the simplest fixed-block recurrence approaches perfect quality while its asymptotic yield vanishes. The paper also develops variable-block ideas and breeding, which uses initially pure pairs as a resource. Later unseeded one-way hashing is a distinct contribution. The threshold above one-half fidelity is sufficient for the stated two-qubit route; it is not a complete test for every entangled state in every dimension. Ideal local operations are another important assumption.\n\n## Follow the resource ledger\n\nAsk your agent to trace one recurrence step from the original paper and list input pairs, local operations, messages, acceptance rule and surviving output. Keep the fidelity calculation separate from the number of accepted pairs. If the source does not specify a practical hardware cost, mark it unknown. This small ledger is reusable: it prevents a later summary from quietly converting a purification protocol into free entanglement or a solved optimal communication capacity.\n\n## Scientific scope\n\nFidelity above one half is sufficient for this two-qubit protocol, not a complete higher-dimensional distillability criterion. Fixed-block recurrence alone has vanishing yield in the perfect-output limit; the positive-rate construction adds variable blocks and breeding resources. The later unseeded one-way hashing protocol is a separate contribution. Ideal local operations and classical messages are assumed; optimal yield is not determined.\n\n## Sources for this explanation\n\n- [Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels](https://arxiv.org/abs/quant-ph/9511027v2): Original exact-version statement, construction and limitations; source-specific byline and contribution scope retained.\n", "summary": "Local operations coordinated by classical messages can distill fewer high-quality entangled pairs from many imperfect two-qubit pairs whose singlet fidelity exceeds one half. The work introduces two-way recurrence purification and seeded asymptotic breeding, providing entanglement that can support faithful teleportation across a noisy link.", "title": "Bennett et al.: distilling noisy entanglement for faithful teleportation" }, "record_id": "urn:uuid:ade3abcf-69d2-4201-ae91-9ffae23f549b", "version": 1, "source_ref": { "record_id": "urn:uuid:ade3abcf-69d2-4201-ae91-9ffae23f549b", "version": 1, "content_hash": "sha256:7a5c7e7c4d2387940a0a960a76ebea5f77a1d6b355c6aa87eb344162f8bc9bdc" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:5a792bfa09fc47f50806e7a85a36af856f1859fdcf47a8e4f88246c98bdee7fe" }, "target": { "record_id": "urn:uuid:ade3abcf-69d2-4201-ae91-9ffae23f549b", "version": 1, "content_hash": "sha256:7a5c7e7c4d2387940a0a960a76ebea5f77a1d6b355c6aa87eb344162f8bc9bdc" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "bennett-et-al-noisy-entanglement-purification-1995", "entry_id": "bennett-et-al-noisy-entanglement-purification-1995", "revision": 1, "title": "Bennett et al.: distilling noisy entanglement for faithful teleportation", "context": "Quantum communication and entanglement", "track": "Exact theorem and reusable mathematical method", "band": "A", "modifier": "+", "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-10-23", "evidence_cutoff": "2026-10-23", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "Local operations coordinated by classical messages can distill fewer high-quality entangled pairs from many imperfect two-qubit pairs whose singlet fidelity exceeds one half. The work introduces two-way recurrence purification and seeded asymptotic breeding, providing entanglement that can support faithful teleportation across a noisy link.", "scope": "Local operations coordinated by classical messages can distill fewer high-quality entangled pairs from many imperfect two-qubit pairs whose singlet fidelity exceeds one half. The work introduces two-way recurrence purification and seeded asymptotic breeding, providing entanglement that can support faithful teleportation across a noisy link. Fidelity above one half is sufficient for this two-qubit protocol, not a complete higher-dimensional distillability criterion. Fixed-block recurrence alone has vanishing yield in the perfect-output limit; the positive-rate construction adds variable blocks and breeding resources. The later unseeded one-way hashing protocol is a separate contribution. Ideal local operations and classical messages are assumed; optimal yield is not determined.", "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. Fidelity above one half is sufficient for this two-qubit protocol, not a complete higher-dimensional distillability criterion. Fixed-block recurrence alone has vanishing yield in the perfect-output limit; the positive-rate construction adds variable blocks and breeding resources. The later unseeded one-way hashing protocol is a separate contribution. Ideal local operations and classical messages are assumed; optimal yield is not determined.", "references": [ { "title": "Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels", "url": "https://arxiv.org/abs/quant-ph/9511027v2", "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:ade3abcf-69d2-4201-ae91-9ffae23f549b", "version": 1, "content_hash": "sha256:7a5c7e7c4d2387940a0a960a76ebea5f77a1d6b355c6aa87eb344162f8bc9bdc" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "150000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": { "id": "bennett-et-al-noisy-entanglement-purification-1995", "target": { "record_id": "urn:uuid:ade3abcf-69d2-4201-ae91-9ffae23f549b", "version": 1, "content_hash": "sha256:7a5c7e7c4d2387940a0a960a76ebea5f77a1d6b355c6aa87eb344162f8bc9bdc" }, "sections": [ { "title": "Can noisy entanglement be cleaned?", "text": "Imagine two laboratories sharing many imperfect quantum pairs. A perfect pair could support teleportation, but noise has weakened the shared resource. Bennett and colleagues showed how the laboratories can sacrifice some pairs to improve others using local operations and ordinary classical messages. They do not send an unknown quantum state through the classical messages. The existing entanglement remains essential, and teleportation itself comes from earlier work rather than being invented again in this purification protocol." }, { "title": "Keep some pairs and discard others", "text": "The recurrence procedure combines two pairs, measures selected particles and compares the outcomes. Depending on those outcomes, the laboratories keep a surviving pair or discard it. The selected population can have higher singlet fidelity, meaning greater overlap with a chosen ideal entangled state. This is selection with a resource cost, not a way to improve every individual pair for free. Communicating the comparison results is part of the procedure." }, { "title": "Quality and quantity are separate numbers", "text": "For an invented input with singlet fidelity 0.8 in the paper's symmetric two-qubit family, the recurrence expression gives a kept-pair fidelity of about 0.838. That is an increase in quality, conditional on the stated protocol and selection. It does not mean 83.8 percent of the original pairs survive. Two input pairs are consumed in each trial, and some trials are rejected. Fidelity, acceptance probability and final yield answer different questions." }, { "title": "Why one improved pair is not the whole theorem", "text": "Repeating the simplest fixed-block recurrence approaches perfect quality while its asymptotic yield vanishes. The paper also develops variable-block ideas and breeding, which uses initially pure pairs as a resource. Later unseeded one-way hashing is a distinct contribution. The threshold above one-half fidelity is sufficient for the stated two-qubit route; it is not a complete test for every entangled state in every dimension. Ideal local operations are another important assumption." }, { "title": "Follow the resource ledger", "text": "Ask your agent to trace one recurrence step from the original paper and list input pairs, local operations, messages, acceptance rule and surviving output. Keep the fidelity calculation separate from the number of accepted pairs. If the source does not specify a practical hardware cost, mark it unknown. This small ledger is reusable: it prevents a later summary from quietly converting a purification protocol into free entanglement or a solved optimal communication capacity." } ], "references": [ { "title": "Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels", "url": "https://arxiv.org/abs/quant-ph/9511027v2", "locator": "Original exact-version statement, construction and limitations; source-specific byline and contribution scope retained." } ] }, "reading_status": "EXPLANATORY_GUIDE" }