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DTSTART:20250309T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20251120T160000
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URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-209
SUMMARY:Analysis Seminar
CLASS:PUBLIC
DESCRIPTION:JENNIFER ZHU\, UNIVERSITY OF WATERLOO\n\n_Limits of Quantum Gra
 phs_\n\nQuantum graphs were originally introduced as confusability graphs 
 of\nquantum channels by Duan\, Severini\, and Winter. Weaver generalized a
 \nquantum graph to any weak-* closed operator system $\\mathcal V\n\\subse
 teq B(\\mathcal H)$ that is bimodule over the commutant of some\nvon Neuma
 nn algebra $\\mathcal M \\subseteq B(\\mathcal H)$. To date\,\nthere seem 
 to be two notions of quantum graph morphism. Weaver\nintroduced and Daws e
 xtended a notion of CP morphism of quantum\ngraphs. Musto\, Reutter\, and 
 Verdon have also defined classical\nmorphisms of quantum graphs in finite 
 dimensions which agrees with CP\nmorphisms in finite dimensions. Notably\,
  however\, these morphisms are\nnot UCP maps between operator systems of t
 he respective quantum\ngraphs.\n\n      Using a characterizati
 on of quantum relations as\nleft ideals in the extended Haagerup tensor pr
 oduct\, we will obtain a\nnotion of quantum graph morphism (and hence limi
 t) using the\ncategories of von Neumann algebras and operator spaces. Time
 \npermitting\, we will show that this limit recovers profinite classical\n
 graphs.\n\nQNC 1507
DTSTAMP:20260501T165614Z
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