{"paper":{"title":"Violations of the Leggett-Garg inequality in Hybrid Liouvillian Dynamics: The Nonlinear Role of Detector Efficiency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Even an infinitesimal detector efficiency causes a rapid nonlinear suppression of Leggett-Garg inequality violations from their algebraic maximum of 3 to the classical bound.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Parveen Kumar, Sourav Paul, Sourin Das","submitted_at":"2026-05-13T13:18:40Z","abstract_excerpt":"Violations of the Leggett-Garg inequality (LGI) up to its algebraic bound under non-Hermitian dynamics are well established theoretically. Here, we demonstrate that such extreme violations are intrinsically fragile when realistic measurement processes are taken into account. We consider an open two-level system described by a time-local hybrid Liouvillian, with a continuous parameter $q \\in [0,1]$, representing detector efficiency, i.e., the fraction of quantum jump trajectories that are retained in the ensemble. This parameter interpolates between trace-preserving Lindblad dynamics ($q=1$) an"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"While K3 approaches its algebraic maximum of 3 in the null-efficiency limit, even an infinitesimal increase in detector efficiency induces a rapid, highly nonlinear suppression toward the classical bound.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The time-local hybrid Liouvillian with continuous parameter q accurately captures realistic measurement processes that interpolate between full Lindblad dynamics and no-jump non-Hermitian evolution.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Detector efficiency causes rapid nonlinear suppression of extreme Leggett-Garg inequality violations in hybrid Liouvillian dynamics.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Even an infinitesimal detector efficiency causes a rapid nonlinear suppression of Leggett-Garg inequality violations from their algebraic maximum of 3 to the classical bound.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"731da7fcd253d38fc5f222433dc58c7b8545bcb75725db333776c16fcea613e5"},"source":{"id":"2605.13494","kind":"arxiv","version":1},"verdict":{"id":"3e348bf2-7c1c-404b-8b7f-9296288a8135","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:55:35.844963Z","strongest_claim":"While K3 approaches its algebraic maximum of 3 in the null-efficiency limit, even an infinitesimal increase in detector efficiency induces a rapid, highly nonlinear suppression toward the classical bound.","one_line_summary":"Detector efficiency causes rapid nonlinear suppression of extreme Leggett-Garg inequality violations in hybrid Liouvillian dynamics.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The time-local hybrid Liouvillian with continuous parameter q accurately captures realistic measurement processes that interpolate between full Lindblad dynamics and no-jump non-Hermitian evolution.","pith_extraction_headline":"Even an infinitesimal detector efficiency causes a rapid nonlinear suppression of Leggett-Garg inequality violations from their algebraic maximum of 3 to the classical bound."},"references":{"count":56,"sample":[{"doi":"","year":2002,"title":"A. J. Leggett, J. Phys.: Condens. Matter14, R415 (2002)","work_id":"b29644c1-2209-4acc-a299-45d41ee78b24","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"M. Schlosshauer, Rev. Mod. Phys.76, 1267 (2005)","work_id":"dd5f1921-ccca-4408-b712-a063ab3892c1","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"W. H. Zurek, Rev. Mod. Phys.75, 715 (2003)","work_id":"55c1f0fb-a91d-4a1a-b31d-40e410d5030b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"J. Kofler and C. Brukner, Phys. Rev. Lett.99, 180403 (2007)","work_id":"e6e22554-48f7-4abc-b93c-58ebc3c81e59","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1985,"title":"A. J. Leggett and A. Garg, Phys. Rev. Lett.54, 857 (1985)","work_id":"b5dc23a3-9f70-4395-82b2-5c662d1ff284","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":56,"snapshot_sha256":"10511943f7c3fe7db385dc87f37766e7e7ba0dc13fa9553df5175a527138002e","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9bba6810eb431cc33d9eaf9e9c384fe68b41076dac85d41460b170f1bf552d0f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}