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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20240806T083000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-thesis-defence-35
SUMMARY:PhD Thesis Defence
CLASS:PUBLIC
DESCRIPTION:YUMING ZHAO\, DEPARTMENT OF PURE MATHEMATICS\, UNIVERSITY OF WA
 TERLOO \n\n“Tsirelson's Bound and Beyond: Verifiability and Complexity 
 in\nQuantum Systems” \n\nSuppose we have a physical system consisting o
 f two separate labs\,\neach can mark several measurements. If the two labs
  are entangled\,\nthen their measurement statistics can be correlated in s
 urprising\nways. In general\, we do not directly see the entangled state a
 nd\nmeasurement operators\, only the resulting correlations. There are\nty
 pically many different models achieving a given correlation\, hence\nit is
  remarkable that some correlations have a unique quantum model. A\ncorrela
 tion with this property is called a self-test. In the first\npart of this 
 thesis\, we give a new definition of self-testing in terms\nof states on C
 *-algebras. We show that this operator-algebraic\ndefinition of self-testi
 ng is equivalent to the standard one and\nnaturally extends to the commuti
 ng operator framework for nonlocal\ncorrelations. We also give an operator
 -algebraic formulation of robust\nself-testing in terms of tracial states 
 on C*-algebras.\n\nSelf-testing provides a powerful tool for verifying qua
 ntum\ncomputations. In the second part of this thesis\, we propose a new\n
 model of delegated quantum computation where the client trusts only\nits c
 lassical processing and can verify the server's quantum\ncomputation\, and
  the server can conceal the inner workings of their\nquantum devices. This
  delegation protocol also yields the first\ntwo-prover one-round zero-know
 ledge proof systems of QMA.\n\nMathematically\, bipartite measurements can
  be modeled by the tensor\nproduct of free *-algebras. Many problems for n
 onlocal correlations\nare closely related to deciding whether an element o
 f these algebras\nis positive and finding certificates of positivity. In t
 he third part\nof this thesis\, we show that it is undecidable (coRE-hard)
  to\ndetermine whether a noncommutative polynomial of the tensor product o
 f\nfree *-algebras is positive.\n\nQNC 2101 
DTSTAMP:20260505T000610Z
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