{"id":"W2952493240","doi":"10.48550/arxiv.quant-ph/0411077","title":"Notes on super-operator norms induced by Schatten norms","year":2004,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Quantum Information and Cryptography","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Operator (biology); Operator norm; Mathematics; Norm (philosophy); Hermitian matrix; Pure mathematics; Quasinormal operator; Nuclear operator; Finite-rank operator; Identity (music); Value (mathematics); Algebra over a field; Operator theory; Physics; Epistemology; Statistics; Banach space; Philosophy","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0002954762,0.0005665688,0.0004786675,0.000387186,0.0002626086,0.0004957635,0.002177278,0.0004915317,0.00009720076],"category_scores_gemma":[0.00007538016,0.0004470211,0.0003121169,0.0005576405,0.00008339994,0.0008395651,0.001052716,0.001144878,0.002160368],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001307209,"about_ca_system_score_gemma":0.000310316,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002264476,"about_ca_topic_score_gemma":0.00002008063,"domain_scores_codex":[0.9972757,0.0000525158,0.0006400559,0.0008115385,0.0006419437,0.0005782222],"domain_scores_gemma":[0.9975531,0.00007030817,0.0002624804,0.001628321,0.0001987124,0.0002870443],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.0002264376,0.003855946,0.6023502,0.001752051,0.001632943,0.0001933848,0.03256352,0.006602703,0.04230259,0.2077285,0.02867669,0.07211512],"study_design_scores_gemma":[0.008042805,0.002432902,0.6244708,0.002248339,0.0001512324,0.00006597608,0.0007465459,0.01714049,0.2626677,0.01870774,0.0532484,0.01007705],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9682961,0.0001068181,0.02360881,0.003736795,0.0015015,0.0004266596,0.00003191441,0.0005279966,0.001763366],"genre_scores_gemma":[0.9932231,0.00007203448,0.0009812972,0.005273222,0.0001667308,0.00009064703,0.00009786665,0.00003339199,0.00006167724],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2203651,"threshold_uncertainty_score":0.9997982,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03653159851594198,"score_gpt":0.2584717782121843,"score_spread":0.2219401796962423,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}