{"paper":{"title":"Purification of a monitored qubit: exact path-integral solution","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Purification of a monitored qubit reduces to an exactly solvable multiplicative Langevin equation for its purity.","cross_cats":["cond-mat.stat-mech"],"primary_cat":"quant-ph","authors_text":"Henrique Santos Lima, Matheus M. R. Poltronieri Martins","submitted_at":"2026-05-12T21:55:51Z","abstract_excerpt":"We investigate the purification dynamics of a single qubit under continuous in time monitoring. By employing a collisional model framework where the system interacts sequentially with ancillary qubits, we describe the conditioned evolution of the density matrix through a stochastic master equation. We show that for initial mixed states, the dynamics reduce to a multiplicative Langevin equation for a single scalar parameter representing the state's purity. This stochastic process is solved exactly using the Onsager-Machlup path integral formalism, allowing us to derive the full probability dist"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"for initial mixed states, the dynamics reduce to a multiplicative Langevin equation for a single scalar parameter representing the state's purity. This stochastic process is solved exactly using the Onsager-Machlup path integral formalism, allowing us to derive the full probability distribution for the qubit's trajectories.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The collisional model of sequential interactions with ancillary qubits faithfully captures continuous-in-time monitoring, and the conditioned evolution of the density matrix can be fully reduced to a single scalar purity parameter without loss of essential information.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact Onsager-Machlup path-integral solution for monitored qubit purification reveals a crossover from diffusion-dominated to measurement-dominated regimes with emergent bimodal purity distributions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Purification of a monitored qubit reduces to an exactly solvable multiplicative Langevin equation for its purity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"93acfee97293d5ef0d996d90face3af4a9bef63676a6d5d9f0b3ba6f3fac79d3"},"source":{"id":"2605.12783","kind":"arxiv","version":1},"verdict":{"id":"16407cc3-460f-4cb6-853a-02170ebf3667","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:56:46.389254Z","strongest_claim":"for initial mixed states, the dynamics reduce to a multiplicative Langevin equation for a single scalar parameter representing the state's purity. This stochastic process is solved exactly using the Onsager-Machlup path integral formalism, allowing us to derive the full probability distribution for the qubit's trajectories.","one_line_summary":"Exact Onsager-Machlup path-integral solution for monitored qubit purification reveals a crossover from diffusion-dominated to measurement-dominated regimes with emergent bimodal purity distributions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The collisional model of sequential interactions with ancillary qubits faithfully captures continuous-in-time monitoring, and the conditioned evolution of the density matrix can be fully reduced to a single scalar purity parameter without loss of essential information.","pith_extraction_headline":"Purification of a monitored qubit reduces to an exactly solvable multiplicative Langevin equation for its purity."},"references":{"count":32,"sample":[{"doi":"","year":2018,"title":"Y. Li, X. Chen, and M. P. A. 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X10, 041020 (2020)","work_id":"f012751e-5233-4696-a7ce-d27024ce2207","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Lud- wig,Measurement-induced criticality in random quantum circuits, Phys. Rev. B101, 104302 (2020)","work_id":"4517e4a4-e8cb-49f0-a140-52a7d2a74174","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":32,"snapshot_sha256":"ed4cb6db1c4492d2174008c87b243d50ac2b057c026a4330e23ed11f41ec63bc","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"}