{"id":"W2261386100","doi":"10.26421/qic15.15-16-1","title":"Galois unitaries, mutually unbiased bases, and mub-balanced states","year":2015,"lang":"en","type":"article","venue":"Quantum Information and Computation","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"Perimeter Institute; University of Waterloo","funders":"Army Research Office; Natural Sciences and Engineering Research Council of Canada; Intelligence Advanced Research Projects Activity","keywords":"Mutually unbiased bases; Mathematics; Prime (order theory); Field (mathematics); Conjecture; Pure mathematics; Discrete mathematics; Dimension (graph theory); Hilbert space; Combinatorics","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":[],"consensus_categories":[],"category_scores_codex":[0.0002110229,0.0001229286,0.0001520708,0.00008334665,0.0001066679,0.0001489933,0.00004764856,0.00006262874,0.000007789359],"category_scores_gemma":[0.0001646132,0.0001094819,0.00001607338,0.0001176714,0.00004648258,0.0006923857,0.00003477093,0.00007716328,0.000006683551],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003354321,"about_ca_system_score_gemma":0.00007017286,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001087702,"about_ca_topic_score_gemma":0.00000858652,"domain_scores_codex":[0.9992015,0.00004126389,0.0003228893,0.00008696113,0.0002210981,0.000126307],"domain_scores_gemma":[0.9992743,0.0001471887,0.0001673113,0.00008234462,0.0002116274,0.0001171989],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00009046147,0.00001768378,0.0002750353,0.00008778861,0.00002026882,7.199004e-7,0.006317814,0.0007986907,0.000002345989,0.9740744,0.003178309,0.01513644],"study_design_scores_gemma":[0.001259696,0.0001339761,0.0007330168,0.00001937478,0.00001518671,0.000009693197,0.001897655,0.2318338,0.00001941728,0.7617742,0.002156943,0.0001470392],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.941806,0.00007080236,0.05668789,0.0003016819,0.0002933087,0.0002175564,0.00001068705,0.0001195911,0.0004925171],"genre_scores_gemma":[0.9978668,0.00002322056,0.001530397,0.0003759188,0.00003278695,0.000008136933,0.0001427301,0.000006954176,0.00001303117],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2310351,"threshold_uncertainty_score":0.446454,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04070376796484867,"score_gpt":0.286130497740134,"score_spread":0.2454267297752854,"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."}}