{"id":"W2036400190","doi":"10.1117/12.615759","title":"Mutually unbiased bases, spherical designs, and frames","year":2005,"lang":"en","type":"article","venue":"Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Army Research Office; Mitacs; National Science Foundation","keywords":"Mutually unbiased bases; Dimension (graph theory); Orthonormal basis; Mathematics; Combinatorics; Observable; Discrete mathematics; Prime power; Upper and lower bounds; Prime (order theory); Physics; Pure mathematics; Hilbert space; Quantum mechanics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001819075,0.0007433149,0.0006078809,0.001607188,0.001514811,0.002711164,0.0006364872,0.001086019,0.004815053],"category_scores_gemma":[0.002955959,0.0004685844,0.0006987613,0.001436494,0.004499629,0.002875178,0.001629714,0.001251473,0.001141223],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001540147,"about_ca_system_score_gemma":0.0009521505,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001829111,"about_ca_topic_score_gemma":0.001520862,"domain_scores_codex":[0.9978856,0.0008511972,0.0001071899,0.0004182336,0.0004962689,0.0002414988],"domain_scores_gemma":[0.9990501,0.0003235175,0.000172678,0.0001422954,0.0002132665,0.00009810167],"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":[0.000005430778,0.000001904089,0.00003861202,0.0000209215,0.00000210612,0.000008329094,0.00006572963,0.0005450289,0.0001312887,0.994968,0.0003621712,0.003850462],"study_design_scores_gemma":[0.000006134849,0.00002757415,0.0001333808,0.00003812083,0.000004795222,0.000050068,0.00006694283,0.001564455,0.0003195406,0.9801271,0.01764404,0.00001777554],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1493527,0.02782354,0.5363069,0.003310999,0.0009998244,0.0001716686,0.00105791,0.0004326856,0.2805437],"genre_scores_gemma":[0.807261,0.01269533,0.1445484,0.0009287254,0.001323548,0.0002888344,0.0008135107,0.0001652513,0.0319754],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004815053,"threshold_uncertainty_score":0.01610792,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0267971855973071,"score_gpt":0.2630379645977112,"score_spread":0.2362407790004041,"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."}}