{"paper":{"title":"Channel capacities of classical and quantum list decoding","arxiv_id":"quant-ph/0603031","primary_cat":"quant-ph","submitted_at":"2006-03-04T06:04:55+00:00","version_compiled":"v3"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v3","sentences":[{"i":0,"p":0.79,"id":"s0","own":false,"role":"background","text":"We focus on classical and quantum list decoding.","hedge":{"p":0.76,"label":"asserted"},"own_p":0.25,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.79,"limitation":0.0,"future_work":0.0,"contribution":0.21,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":false,"role":"background","text":"The capacity of list decoding was obtained by Nishimura in the case when the number of list does not increase exponentially.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.03,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.23,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.99,"id":"s2","own":false,"role":"gap","text":"However, the capacity of the exponential-list case is open even in the classical case while its converse part was obtained by Nishimura.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.23,"role_probabilities":{"gap":0.99,"method":0.0,"result":0.0,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.68,"id":"s3","own":true,"role":"contribution","text":"We derive the channel capacities in the classical and quantum case with an exponentially increasing list.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.88,"quantitative":false,"quantitative_p":0.15,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.32,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.68,"interpretation":0.0}},{"i":4,"p":0.92,"id":"s4","own":true,"role":"method","text":"The converse part of the quantum case is obtained by modifying Nagaoka's simple proof for strong converse theorem for channel capacity.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.89,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.92,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.07,"interpretation":0.0}},{"i":5,"p":0.96,"id":"s5","own":true,"role":"method","text":"The direct part is derived by a quite simple argument.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.96,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"We derive the channel capacities in the classical and quantum case with an exponentially increasing list.","location":"abstract s3","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":4715,"cost_usd_reported":0.0},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.17,"states_limitation":0.11,"human_participants":0.01,"controlled_comparison":0.03,"randomized_assignment":0.01,"states_quantitative_result":0.11,"compares_with_prior_results":0.91,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":1.0,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":1.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":1.0,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":1.0,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":1.0,"text":"We derive the channel capacities in the classical and quantum case with an exponentially increasing list.","location":"abstract s3"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v3"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":6,"sentences_in_abstract":6},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; 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