{"id":"W2762174834","doi":"10.22331/q-2018-02-05-51","title":"Characterization of linear maps on<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>M</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>whose multiplicity maps have maximal norm, with an application in quantum information","year":2018,"lang":"lv","type":"article","venue":"Quantum","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Transpose; Multiplicity (mathematics); Characterization (materials science); Bounded function; Quantum; Norm (philosophy); Linear map; Equivalence (formal languages); Operator (biology)","routes":{"ca_aff":true,"ca_fund":true,"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":["insufficient_payload"],"category_scores_codex":[0.001221701,0.0006432257,0.0003945713,0.0004652049,0.000733985,0.0003749173,0.001045093,0.00123673,0.001884375],"category_scores_gemma":[0.0008473145,0.0009736223,0.0003950846,0.0007532608,0.0008057324,0.001935114,0.0005916114,0.001042617,0.00161813],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000492216,"about_ca_system_score_gemma":0.0005200955,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005845419,"about_ca_topic_score_gemma":0.0009299441,"domain_scores_codex":[0.9944789,0.0002254397,0.00178492,0.0009335055,0.001434569,0.00114262],"domain_scores_gemma":[0.9944644,0.0005262533,0.002346789,0.001936966,0.0003171898,0.0004083936],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.001391388,0.0005861048,0.00009715656,0.001351921,0.0002443065,0.00007006027,0.005262464,0.0003036024,0.005789331,0.9813941,0.001435273,0.002074266],"study_design_scores_gemma":[0.002293279,0.002811194,0.00049052,0.001238141,0.0004035485,0.0002190536,0.002221898,0.3676527,0.6015903,0.01749793,0.002327614,0.001253885],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9732794,0.0000497592,0.01665839,0.000287661,0.000879421,0.0001972677,0.000391378,0.000206525,0.008050213],"genre_scores_gemma":[0.9878556,0.0002029601,0.007563868,0.0005388577,0.0009582657,0.0005964148,0.001908499,0.0003194544,0.00005610299],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9638962,"threshold_uncertainty_score":0.9992715,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02143182351678971,"score_gpt":0.2608143640041569,"score_spread":0.2393825404873672,"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."}}