{"paper":{"title":"Performance Guarantees for Quantum Neural Estimation of Entropies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Quantum neural estimators achieve O(d/ε²) copy complexity for measured Rényi relative entropies when density pairs have bounded Thompson metric.","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"quant-ph","authors_text":"Mark M. Wilde, Sreejith Sreekumar, Ziv Goldfeld","submitted_at":"2025-11-24T16:36:06Z","abstract_excerpt":"Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently emerged as an appealing computational framework for estimating these measures. Such estimators combine classical neural networks with parametrized quantum circuits, and their deployment typically entails tedious tuning of hyperparameters controlling the sample size, network architecture, and circuit topology. This work initiates the study of formal guarantees for "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For an appropriate sub-class of density operator pairs on a space of dimension d with bounded Thompson metric, our theory establishes a copy complexity of O(|Θ(U)|d/ε²) for QNE with a quantum circuit parameter set Θ(U), which has minimax optimal dependence on the accuracy ε.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The central bounds rely on the density operator pairs having bounded Thompson metric (or being permutation invariant); without this restriction the stated copy complexity no longer holds and the analysis does not apply.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quantum neural estimators achieve minimax-optimal copy complexity O(|Θ(U)| d / ε²) with sub-Gaussian concentration for measured Rényi relative entropies on density pairs with bounded Thompson metric.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Quantum neural estimators achieve O(d/ε²) copy complexity for measured Rényi relative entropies when density pairs have bounded Thompson metric.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c8f2abed219b06aca4f7e9a7b481273718d539932e10b0b74fe856a57ebfc9d8"},"source":{"id":"2511.19289","kind":"arxiv","version":2},"verdict":{"id":"53caa6ee-1346-47f3-b134-b7af3d552aa3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T05:58:10.676637Z","strongest_claim":"For an appropriate sub-class of density operator pairs on a space of dimension d with bounded Thompson metric, our theory establishes a copy complexity of O(|Θ(U)|d/ε²) for QNE with a quantum circuit parameter set Θ(U), which has minimax optimal dependence on the accuracy ε.","one_line_summary":"Quantum neural estimators achieve minimax-optimal copy complexity O(|Θ(U)| d / ε²) with sub-Gaussian concentration for measured Rényi relative entropies on density pairs with bounded Thompson metric.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The central bounds rely on the density operator pairs having bounded Thompson metric (or being permutation invariant); without this restriction the stated copy complexity no longer holds and the analysis does not apply.","pith_extraction_headline":"Quantum neural estimators achieve O(d/ε²) copy complexity for measured Rényi relative entropies when density pairs have bounded Thompson metric."},"references":{"count":95,"sample":[{"doi":"","year":1927,"title":"J. von Neumann, “Thermodynamik quantenmechanischer gesamtheiten,”Nachrichten von der Gesellschaft der Wis- senschaften zu G ¨ottingen, Mathematisch-Physikalische Klasse, vol. 1927, pp. 273–291, 1927","work_id":"ff57ec28-1aff-49b4-b1bf-8b8cb2b74a28","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1948,"title":"A mathematical theory of communication","work_id":"929c1041-d2c5-4e78-a00a-96fc53c75c47","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1961,"title":"On measures of entropy and information,","work_id":"96e76db9-9100-4dc3-828a-a25f8051c117","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1951,"title":"On information and sufficiency,","work_id":"2ab1c343-14c3-4c4a-9aa5-6f336b9be713","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1962,"title":"Conditional expectations in an operator algebra IV (entropy and information),","work_id":"0cac9cd6-f530-4ff4-b383-dc464c0dca68","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":95,"snapshot_sha256":"a9dcadbe6a0d7b2c0906865435b4fed9b8721ff3a917b7e8d2fe40b30c7f4e50","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"dcc6acbd3e8f16539c5f7000d54bf83e45c147ace44ac2bd5aadb04e931cc90d"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}