Abstract

Van Dam and Haydon looked at the task of ``catalytically producing entanglement”, argued that in the usual tensor model it could not be achieved in the usual tensor model but also showed that given any margin of error one could convince an observer that it had been accomplished. In our work with R. CLeve and L.Liu we proved that one could accomplish this task in the commuting model.  Our prof used L. Brown’s non-commuting unitary C-algebra which is very akin to the C-algebra of the quantum group U_n^+. S. Harris showed questions about Brown’s algebra arising from this work are equivalent to  Connes’ Embedding Probelm(CEP). This led to a theory of unitary correlation sets that parallels Tsirelson’s problems and yields another equivalence to CEP . We will also look at later work that considers the task of catalytically producing the catalytic state and of recent work about universal embezzlement which shows type III -1 factors are needed.