{"id":"W2071160621","doi":"10.1007/s00220-008-0624-0","title":"Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p &gt; 1","year":2008,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Wireless Communication Security Techniques","field":"Engineering","cited_by":113,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"Engineering and Physical Sciences Research Council","keywords":"Counterexample; Conjecture; Von Neumann entropy; Quantum; Classical capacity; Entropy (arrow of time); Quantum channel; Quantum mutual information; Joint quantum entropy","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00307131,0.001057036,0.001252249,0.001808307,0.005249291,0.0065689,0.002257161,0.004135077,0.01557261],"category_scores_gemma":[0.01661351,0.0008681022,0.001150596,0.002094944,0.009603287,0.01154933,0.00683212,0.006621852,0.001435295],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001559399,"about_ca_system_score_gemma":0.0008797001,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007606398,"about_ca_topic_score_gemma":0.0005432123,"domain_scores_codex":[0.9965391,0.001056248,0.000174896,0.0007881626,0.0008109631,0.0006307029],"domain_scores_gemma":[0.9894813,0.007123632,0.000668853,0.001111481,0.0007507333,0.0008639853],"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":[0.00006697818,0.00001470125,0.0002334502,0.00003560358,0.000005897923,0.00008948621,0.000157002,0.0003031174,0.0002405171,0.993618,0.003993866,0.001241447],"study_design_scores_gemma":[0.00002030749,0.000006987773,0.0001295695,0.00001069111,0.000005503314,0.0001081103,0.00008557472,0.001612492,0.0003001657,0.9957014,0.002010392,0.000008778979],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.433903,0.001654441,0.1197538,0.0494309,0.002117709,0.0001078088,0.001489571,0.001369247,0.3901736],"genre_scores_gemma":[0.9731042,0.0004213436,0.01051992,0.002346508,0.001371726,0.0001328129,0.000626807,0.0001970755,0.0112795],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01557261,"threshold_uncertainty_score":0.05209553,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09462451070217012,"score_gpt":0.3255230945191994,"score_spread":0.2308985838170292,"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."}}