{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "bennett-divincenzo-smolin-wootters-distillation-coding-correspondence-1996", "title": "Bennett et al.: connecting one-way entanglement distillation and quantum error correction", "summary": "The work relates one-way entanglement purification to quantum channel coding and shows that free forward classical messages do not increase unassisted quantum capacity. For Bell-diagonal states and their associated generalized depolarizing channels, the reversible state-channel construction identifies one-way distillable entanglement with quantum capacity.", "boundary": "For a general channel and a general bipartite state the two maps need not be inverses, so the paper gives inequalities rather than a universal equality between arbitrary channel capacity and its Choi-state distillable entanglement. Two-way classical assistance is a different resource and can increase rates. No claim of general additivity or a single-letter capacity formula.", "area": "Quantum information theory", "topic": "Physics", "year": 1996, "lane": "HUMAN", "result": "THEOREM", "package_id": "bennett-divincenzo-smolin-wootters-distillation-coding-correspondence-1996", "target": { "record_id": "urn:uuid:16c7dda5-a71d-403e-a8be-a3670521f3d1", "version": 1, "content_hash": "sha256:8864372425be1e611bbdd4ae8da57f8e9be9adc3ec8079d975575be3ad89478d" }, "humans": [ "Charles H. Bennett", "David P. DiVincenzo", "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-9604024v2", "title": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2", "date": "1996-08-08" } ], "geography": { "country_codes": [ "US" ], "location_basis": "Bennett and DiVincenzo IBM Yorktown Heights, Smolin UCLA and Wootters Williams College US. Original source bylines, not nationality, sovereignty attribution or scientific ownership.", "source_url": "https://arxiv.org/abs/quant-ph/9604024v2", "target": { "record_id": "urn:uuid:16c7dda5-a71d-403e-a8be-a3670521f3d1", "version": 1, "content_hash": "sha256:8864372425be1e611bbdd4ae8da57f8e9be9adc3ec8079d975575be3ad89478d" }, "basis": "RESEARCH_LOCATION_OR_PAPER_AFFILIATION", "reviewed_on": "2026-10-23", "nationality_inferred": false, "sources": [ { "title": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2" } ], "coverage_status": "COMPLETE", "country_labels": { "US": "United States" } }, "points": "240000", "published_grade": { "id": "bennett-divincenzo-smolin-wootters-distillation-coding-correspondence-1996", "entry_id": "bennett-divincenzo-smolin-wootters-distillation-coding-correspondence-1996", "band": "S", "modifier": "-", "target": { "record_id": "urn:uuid:16c7dda5-a71d-403e-a8be-a3670521f3d1", "version": 1, "content_hash": "sha256:8864372425be1e611bbdd4ae8da57f8e9be9adc3ec8079d975575be3ad89478d" }, "what_changed": "The work relates one-way entanglement purification to quantum channel coding and shows that free forward classical messages do not increase unassisted quantum capacity. For Bell-diagonal states and their associated generalized depolarizing channels, the reversible state-channel construction identifies one-way distillable entanglement with quantum capacity.", "scope": "The work relates one-way entanglement purification to quantum channel coding and shows that free forward classical messages do not increase unassisted quantum capacity. For Bell-diagonal states and their associated generalized depolarizing channels, the reversible state-channel construction identifies one-way distillable entanglement with quantum capacity. For a general channel and a general bipartite state the two maps need not be inverses, so the paper gives inequalities rather than a universal equality between arbitrary channel capacity and its Choi-state distillable entanglement. Two-way classical assistance is a different resource and can increase rates. No claim of general additivity or a single-letter capacity formula.", "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:16c7dda5-a71d-403e-a8be-a3670521f3d1", "version": 1, "content_hash": "sha256:8864372425be1e611bbdd4ae8da57f8e9be9adc3ec8079d975575be3ad89478d" }, "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. Bennett", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "prover" ], "source": { "citation": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "David P. DiVincenzo", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "prover" ], "source": { "citation": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "John A. Smolin", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "prover" ], "source": { "citation": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2" } }, { "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": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2" } } ], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2" } } ], "origin": "HUMAN_LEGACY", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "For a general channel and a general bipartite state the two maps need not be inverses, so the paper gives inequalities rather than a universal equality between arbitrary channel capacity and its Choi-state distillable entanglement. Two-way classical assistance is a different resource and can increase rates. No claim of general additivity or a single-letter capacity formula.", "domain": "Quantum information theory" }, "sources": [ { "citation": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2" } ], "statement": "# Bennett et al.: connecting one-way entanglement distillation and quantum error correction\n\n## Two pictures of the same protection problem\n\nA quantum error-correcting code protects information during noisy storage or transmission. Entanglement distillation starts with noisy shared pairs and tries to recover cleaner pairs. Bennett, DiVincenzo, Smolin and Wootters connected these pictures operationally. A suitable one-way purification procedure can become a communication code, while coding can support a corresponding purification route. The connection lets a method discovered in one picture become useful in another, without pretending that every mathematical quantity is automatically identical.\n\n## Learn about the errors by sacrificing pairs\n\nTheir hashing method considers many independent pairs drawn from a known Bell-diagonal mixture. Bell states are four standard maximally entangled two-qubit states. Carefully chosen local operations and measurements reveal parity information about which errors occurred. Some pairs are consumed to obtain that information; the remaining pairs can then be corrected. The method borrows the organizing idea of random hashing, but must account for how quantum operations also change the unmeasured pairs.\n\n## What does one minus entropy mean?\n\nConsider an invented mixture using only two Bell states with probabilities 0.9 and 0.1. Its binary entropy is about 0.469 bits per pair. The asymptotic hashing expression therefore gives about 0.531 output pairs per input pair under the ideal independent-input model. This is an achievable rate, not the exact optimum for every protocol. Finite blocks need additional allowance for uncertainty and failure; one thousand input pairs do not guarantee exactly 531 perfect outputs.\n\n## Do not erase the direction of communication\n\nForward classical messages do not increase the unassisted quantum capacity in the setting considered. Two-way assistance can change the answer substantially. The reversible equality between a state's one-way distillable entanglement and a channel's quantum capacity applies to the specified Bell-diagonal and generalized-depolarizing correspondence. For arbitrary states and channels the source instead provides inequalities. Dropping those conditions would turn a useful bridge into an incorrect universal capacity formula.\n\n## Build a map that another reader can reuse\n\nGive your agent three boxes labelled shared state, communication channel and allowed classical messages. Ask it to attach each source statement to the correct box and draw only the conversions actually justified. Record which arrows give an inequality and which special case gives equality. Include exact pages and leave unknown rates unknown. That diagram is a manageable contribution without independently solving the optimal capacity problem or running a quantum computer.\n\n## Scientific scope\n\nFor a general channel and a general bipartite state the two maps need not be inverses, so the paper gives inequalities rather than a universal equality between arbitrary channel capacity and its Choi-state distillable entanglement. Two-way classical assistance is a different resource and can increase rates. No claim of general additivity or a single-letter capacity formula.\n\n## Sources for this explanation\n\n- [Mixed State Entanglement and Quantum Error Correction](https://arxiv.org/abs/quant-ph/9604024v2): Original exact-version statement, construction and limitations; source-specific byline and contribution scope retained.\n", "summary": "The work relates one-way entanglement purification to quantum channel coding and shows that free forward classical messages do not increase unassisted quantum capacity. For Bell-diagonal states and their associated generalized depolarizing channels, the reversible state-channel construction identifies one-way distillable entanglement with quantum capacity.", "title": "Bennett et al.: connecting one-way entanglement distillation and quantum error correction" }, "record_id": "urn:uuid:16c7dda5-a71d-403e-a8be-a3670521f3d1", "version": 1, "source_ref": { "record_id": "urn:uuid:16c7dda5-a71d-403e-a8be-a3670521f3d1", "version": 1, "content_hash": "sha256:8864372425be1e611bbdd4ae8da57f8e9be9adc3ec8079d975575be3ad89478d" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:8e705bfb4d478f818a1a547a7f5bc8cbf646986b72c768adc7e5bc478b4143c0" }, "target": { "record_id": "urn:uuid:16c7dda5-a71d-403e-a8be-a3670521f3d1", "version": 1, "content_hash": "sha256:8864372425be1e611bbdd4ae8da57f8e9be9adc3ec8079d975575be3ad89478d" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "bennett-divincenzo-smolin-wootters-distillation-coding-correspondence-1996", "entry_id": "bennett-divincenzo-smolin-wootters-distillation-coding-correspondence-1996", "revision": 1, "title": "Bennett et al.: connecting one-way entanglement distillation and quantum error correction", "context": "Quantum information theory", "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": "The work relates one-way entanglement purification to quantum channel coding and shows that free forward classical messages do not increase unassisted quantum capacity. For Bell-diagonal states and their associated generalized depolarizing channels, the reversible state-channel construction identifies one-way distillable entanglement with quantum capacity.", "scope": "The work relates one-way entanglement purification to quantum channel coding and shows that free forward classical messages do not increase unassisted quantum capacity. For Bell-diagonal states and their associated generalized depolarizing channels, the reversible state-channel construction identifies one-way distillable entanglement with quantum capacity. For a general channel and a general bipartite state the two maps need not be inverses, so the paper gives inequalities rather than a universal equality between arbitrary channel capacity and its Choi-state distillable entanglement. Two-way classical assistance is a different resource and can increase rates. No claim of general additivity or a single-letter capacity formula.", "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. For a general channel and a general bipartite state the two maps need not be inverses, so the paper gives inequalities rather than a universal equality between arbitrary channel capacity and its Choi-state distillable entanglement. Two-way classical assistance is a different resource and can increase rates. No claim of general additivity or a single-letter capacity formula.", "references": [ { "title": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2", "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:16c7dda5-a71d-403e-a8be-a3670521f3d1", "version": 1, "content_hash": "sha256:8864372425be1e611bbdd4ae8da57f8e9be9adc3ec8079d975575be3ad89478d" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "240000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": { "id": "bennett-divincenzo-smolin-wootters-distillation-coding-correspondence-1996", "target": { "record_id": "urn:uuid:16c7dda5-a71d-403e-a8be-a3670521f3d1", "version": 1, "content_hash": "sha256:8864372425be1e611bbdd4ae8da57f8e9be9adc3ec8079d975575be3ad89478d" }, "sections": [ { "title": "Two pictures of the same protection problem", "text": "A quantum error-correcting code protects information during noisy storage or transmission. Entanglement distillation starts with noisy shared pairs and tries to recover cleaner pairs. Bennett, DiVincenzo, Smolin and Wootters connected these pictures operationally. A suitable one-way purification procedure can become a communication code, while coding can support a corresponding purification route. The connection lets a method discovered in one picture become useful in another, without pretending that every mathematical quantity is automatically identical." }, { "title": "Learn about the errors by sacrificing pairs", "text": "Their hashing method considers many independent pairs drawn from a known Bell-diagonal mixture. Bell states are four standard maximally entangled two-qubit states. Carefully chosen local operations and measurements reveal parity information about which errors occurred. Some pairs are consumed to obtain that information; the remaining pairs can then be corrected. The method borrows the organizing idea of random hashing, but must account for how quantum operations also change the unmeasured pairs." }, { "title": "What does one minus entropy mean?", "text": "Consider an invented mixture using only two Bell states with probabilities 0.9 and 0.1. Its binary entropy is about 0.469 bits per pair. The asymptotic hashing expression therefore gives about 0.531 output pairs per input pair under the ideal independent-input model. This is an achievable rate, not the exact optimum for every protocol. Finite blocks need additional allowance for uncertainty and failure; one thousand input pairs do not guarantee exactly 531 perfect outputs." }, { "title": "Do not erase the direction of communication", "text": "Forward classical messages do not increase the unassisted quantum capacity in the setting considered. Two-way assistance can change the answer substantially. The reversible equality between a state's one-way distillable entanglement and a channel's quantum capacity applies to the specified Bell-diagonal and generalized-depolarizing correspondence. For arbitrary states and channels the source instead provides inequalities. Dropping those conditions would turn a useful bridge into an incorrect universal capacity formula." }, { "title": "Build a map that another reader can reuse", "text": "Give your agent three boxes labelled shared state, communication channel and allowed classical messages. Ask it to attach each source statement to the correct box and draw only the conversions actually justified. Record which arrows give an inequality and which special case gives equality. Include exact pages and leave unknown rates unknown. That diagram is a manageable contribution without independently solving the optimal capacity problem or running a quantum computer." } ], "references": [ { "title": "Mixed State Entanglement and Quantum Error Correction", "url": "https://arxiv.org/abs/quant-ph/9604024v2", "locator": "Original exact-version statement, construction and limitations; source-specific byline and contribution scope retained." } ] }, "reading_status": "EXPLANATORY_GUIDE" }