{"paper":{"title":"Permanents in linear optical networks","arxiv_id":"quant-ph/0406127","primary_cat":"quant-ph","submitted_at":"2004-06-18T09:32:19+00:00","version_compiled":"v1"},"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 v1","sentences":[{"i":0,"p":0.97,"id":"s0","own":true,"role":"contribution","text":"We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.93,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.02,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.97,"interpretation":0.0}},{"i":1,"p":0.8,"id":"s1","own":true,"role":"result","text":"In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to the computation of permanents.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.29,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.8,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.2,"interpretation":0.0}},{"i":2,"p":0.99,"id":"s2","own":true,"role":"interpretation","text":"An implication of this remarkable fact is that all calculations that are based on evaluating matrix elements are generically computationally hard.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.61,"main_claim_p":0.66,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.99}},{"i":3,"p":0.94,"id":"s3","own":true,"role":"result","text":"Moreover, quantum mechanics provides simpler derivations of certain matrix analysis results which we exemplify by showing that the permanent of any unitary matrix takes its values across the unit disk in the complex plane.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.39,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.94,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.05,"interpretation":0.01}}]},"compiled":{"main_claim":{"p":0.81,"text":"An implication of this remarkable fact is that all calculations that are based on evaluating matrix elements are generically computationally hard.","location":"abstract s2","hedge_strength":{"p":0.98,"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":3586,"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":0.04,"states_limitation":0.25,"human_participants":0.02,"controlled_comparison":0.01,"randomized_assignment":0.01,"states_quantitative_result":0.28,"compares_with_prior_results":0.08,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.99,"value":"proof or derivation","probabilities":{"argument":0.01,"literature":0.0,"proof_or_derivation":0.99,"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":0.79,"text":"In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to the computation of permanents.","location":"abstract s1"}},"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 v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":4,"sentences_in_abstract":4},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}