{"paper":{"title":"The $\\gamma_c$-Peak: Covariant Recovery on Four Organic Qubit Platforms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The fidelity gain from Petz recovery in covariant quantum error correction reaches its maximum exactly at the entanglement-breaking threshold on organic qubit platforms.","cross_cats":["quant-ph"],"primary_cat":"q-bio.NC","authors_text":"Hikaru Wakaura, Taiki Tanimae","submitted_at":"2026-04-22T09:12:12Z","abstract_excerpt":"The Petz recovery map (1986) provably reverses a noisy quantum channel on a reference state, but its algorithmic relevance to real, dissipation-dominated platforms has remained unclear. Using the open-source \\texttt{organic-qc-bench} simulation package, we benchmark a Petz-style covariant-purification quantum error correction (CQEC) protocol across four engineered organic qubit platforms operated \\emph{without any magnetic field}: a flavin-nitroxide radical-pair reservoir (P1); perchlorotriphenylmethyl radicals in a covalent organic framework (P2); the SVILC qubit [Wakaura2017] on $\\kappa$-(BE"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The fidelity gain Delta F is maximised at the entanglement-breaking threshold gamma_c, with Delta F_max = +0.303 at d=64 and a linear log2 d scaling over d=2-64, algorithmically confirming the prediction that Petz recovery preserves coherence beyond this threshold.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The open-source organic-qc-bench package and its noise models accurately capture the physical dissipation and coherence properties of the four real organic platforms (P1-P4) when operated without magnetic fields; the SVILC qubit on platform P3 is assumed confirmed.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Simulations across four organic qubit platforms show Petz recovery yields maximum fidelity gain at the entanglement-breaking threshold gamma_c, with Delta F max of 0.303 at dimension 64 and log2 d scaling.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The fidelity gain from Petz recovery in covariant quantum error correction reaches its maximum exactly at the entanglement-breaking threshold on organic qubit platforms.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5d083a819a7b368737f3ed3d1c7dc38a7b315f70f261028652b120aa2bc1a4e0"},"source":{"id":"2605.00026","kind":"arxiv","version":3},"verdict":{"id":"79692613-003a-49be-814f-02ba6c7077cf","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:20:43.216142Z","strongest_claim":"The fidelity gain Delta F is maximised at the entanglement-breaking threshold gamma_c, with Delta F_max = +0.303 at d=64 and a linear log2 d scaling over d=2-64, algorithmically confirming the prediction that Petz recovery preserves coherence beyond this threshold.","one_line_summary":"Simulations across four organic qubit platforms show Petz recovery yields maximum fidelity gain at the entanglement-breaking threshold gamma_c, with Delta F max of 0.303 at dimension 64 and log2 d scaling.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The open-source organic-qc-bench package and its noise models accurately capture the physical dissipation and coherence properties of the four real organic platforms (P1-P4) when operated without magnetic fields; the SVILC qubit on platform P3 is assumed confirmed.","pith_extraction_headline":"The fidelity gain from Petz recovery in covariant quantum error correction reaches its maximum exactly at the entanglement-breaking threshold on organic qubit platforms."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":41,"sample":[{"doi":"","year":2017,"title":"Ex- ternal current as a coupler between the spin-vortex-induced loop current qubits","work_id":"df6512d0-e52d-410c-aa6a-9dc666689428","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"3-Layer Quantum Brain Hypothesis: Covariant Error Correction, Dynamical Decoupling and Petz Recovery in Biological Radical-Pair Systems","work_id":"217ccc65-f86d-4a24-9968-12cd2ea23b91","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"The radical-pair mechanism of magnetorecep- tion","work_id":"d8315877-e1cf-4732-8c4c-cdaddc148d08","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1986,"title":"Sufficient subalgebras and the relative entropy of states of a von neumann algebra","work_id":"07a66e95-b382-4008-a6bb-cbe7bd4bcabf","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"Harness- ing nonlinearity: Predicting chaotic systems and saving energy in wireless communica- tion","work_id":"1231b99c-21da-466f-8e93-f21d0dded108","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":41,"snapshot_sha256":"8f5c2852e913ad89fbdc7f6cd07ac1910378c8ffa78f500c72de87eb8454ee4e","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"dc2d582fdb7be63a0187d4e795a1548c64b4efebd0b74705bcb90335acbfdab2"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}