{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:TJ5YINI5KIIFALFHQKSMWXDAP4","short_pith_number":"pith:TJ5YINI5","schema_version":"1.0","canonical_sha256":"9a7b84351d5210502ca782a4cb5c607f04003fdb3d20e525ef0019adb4ca60c3","source":{"kind":"arxiv","id":"2404.09014","version":2},"attestation_state":"computed","paper":{"title":"Lower bounds on bipartite entanglement in noisy graph states","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Certain graph states keep strictly positive coherent information under any non-maximal depolarizing noise in the pre-edge model.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Aqil Sajjad, Don Towsley, Eneet Kaur, Kenneth Goodenough, Saikat Guha","submitted_at":"2024-04-13T14:01:45Z","abstract_excerpt":"Graph states are a key resource for a number of applications in quantum information theory. Due to the inherent noise in noisy intermediate-scale quantum (NISQ) era devices, it is important to understand the effects noise has on the usefulness of graph states. We consider a noise model where the initial qubits undergo depolarizing noise before the application of the CZ operations that generate edges between qubits situated at the nodes of the resulting graph state. For this model we develop a method for calculating the coherent information -- a lower bound on the rate at which entanglement can"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2404.09014","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2024-04-13T14:01:45Z","cross_cats_sorted":[],"title_canon_sha256":"29b13ccdb3933166c3913809deb04273292f62e181aab6e506fb983b88c85df2","abstract_canon_sha256":"c9436ddd295ddb861250822df70feed03c38917e79eaca7ffc7436d9b66a8d2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T14:06:35.497021Z","signature_b64":"VjtQAHM13klic43kIpCCLsMPXdqhfmTTUZdAG9qnpw2S2sAgWQKPowPzLDSxRzARCLHXCTt3TGtYNj115gZSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a7b84351d5210502ca782a4cb5c607f04003fdb3d20e525ef0019adb4ca60c3","last_reissued_at":"2026-05-27T14:06:35.495954Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T14:06:35.495954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower bounds on bipartite entanglement in noisy graph states","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Certain graph states keep strictly positive coherent information under any non-maximal depolarizing noise in the pre-edge model.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Aqil Sajjad, Don Towsley, Eneet Kaur, Kenneth Goodenough, Saikat Guha","submitted_at":"2024-04-13T14:01:45Z","abstract_excerpt":"Graph states are a key resource for a number of applications in quantum information theory. Due to the inherent noise in noisy intermediate-scale quantum (NISQ) era devices, it is important to understand the effects noise has on the usefulness of graph states. We consider a noise model where the initial qubits undergo depolarizing noise before the application of the CZ operations that generate edges between qubits situated at the nodes of the resulting graph state. For this model we develop a method for calculating the coherent information -- a lower bound on the rate at which entanglement can"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We find a family of graph states that maintain a strictly positive coherent information for any amount of (non-maximal) depolarizing noise.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The specific noise model in which depolarizing noise acts independently on each initial qubit before the CZ operations that create the graph edges (as stated in the abstract's description of the model considered).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Develops a calculation method for coherent information lower bounds on bipartite entanglement in graph states with pre-CZ depolarizing noise and identifies a family maintaining strictly positive coherent information for any non-maximal noise level.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Certain graph states keep strictly positive coherent information under any non-maximal depolarizing noise in the pre-edge model.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"905f2c6ee3e31196ea621ed182f3155c8a27934aaa218bf008ba2d7bf07e8e96"},"source":{"id":"2404.09014","kind":"arxiv","version":2},"verdict":{"id":"cc7e1612-b4f4-43dd-b9a8-30062513cfc9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T02:20:03.308682Z","strongest_claim":"We find a family of graph states that maintain a strictly positive coherent information for any amount of (non-maximal) depolarizing noise.","one_line_summary":"Develops a calculation method for coherent information lower bounds on bipartite entanglement in graph states with pre-CZ depolarizing noise and identifies a family maintaining strictly positive coherent information for any non-maximal noise level.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The specific noise model in which depolarizing noise acts independently on each initial qubit before the CZ operations that create the graph edges (as stated in the abstract's description of the model considered).","pith_extraction_headline":"Certain graph states keep strictly positive coherent information under any non-maximal depolarizing noise in the pre-edge model."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.09014/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":28,"sample":[{"doi":"","year":null,"title":"Therefore, nB = 1 maximizes IA","work_id":"ef116e05-b435-4610-a3d9-c86744981ee7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Given nB, IA is an increasing function of nA, which Asymptotically converges from below to a constant value for a given P ̸= 0 and P ̸= 1","work_id":"6cb43943-a3f1-4e6f-9e76-89a8ac343a47","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"We show in Fig","work_id":"e7396649-5d01-4029-bd96-0d039e4f6cff","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"This gives H(ρA) = f1(1, P) = 1, with coherent information IA = 1 − nH2(P)","work_id":"ae0ed637-dff5-494b-9a72-6260622f592c","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"When nA > nB, IA > IB and vice versa. That is, for any fully connected graph, the side hav- ing the largest number of qubits has the highest subsystem entropy (since f1(nA, P) > f1(nB, P) when nA > nB","work_id":"a3b6b46e-4a69-4aa1-a29a-bb72418a6f10","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":28,"snapshot_sha256":"468d2bae469e585e8c1d947f78af1e026e2e98a1eec5a3d0e5cfd686f89d9113","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2404.09014","created_at":"2026-05-27T14:06:35.496109+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.09014v2","created_at":"2026-05-27T14:06:35.496109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.09014","created_at":"2026-05-27T14:06:35.496109+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJ5YINI5KIIF","created_at":"2026-05-27T14:06:35.496109+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJ5YINI5KIIFALFH","created_at":"2026-05-27T14:06:35.496109+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJ5YINI5","created_at":"2026-05-27T14:06:35.496109+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4","json":"https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4.json","graph_json":"https://pith.science/api/pith-number/TJ5YINI5KIIFALFHQKSMWXDAP4/graph.json","events_json":"https://pith.science/api/pith-number/TJ5YINI5KIIFALFHQKSMWXDAP4/events.json","paper":"https://pith.science/paper/TJ5YINI5"},"agent_actions":{"view_html":"https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4","download_json":"https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4.json","view_paper":"https://pith.science/paper/TJ5YINI5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.09014&json=true","fetch_graph":"https://pith.science/api/pith-number/TJ5YINI5KIIFALFHQKSMWXDAP4/graph.json","fetch_events":"https://pith.science/api/pith-number/TJ5YINI5KIIFALFHQKSMWXDAP4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4/action/storage_attestation","attest_author":"https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4/action/author_attestation","sign_citation":"https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4/action/citation_signature","submit_replication":"https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4/action/replication_record"}},"created_at":"2026-05-27T14:06:35.496109+00:00","updated_at":"2026-05-27T14:06:35.496109+00:00"}