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DTSTART;TZID=America/Toronto:20250410T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-oral-defence
SUMMARY:PhD Oral Defence
CLASS:PUBLIC
DESCRIPTION:ADINA GOLDBERG\, UNIVERSITY OF WATERLOO\n\n_Synchronous and qua
 ntum games: Graphical and algebraic methods_\n\nThis is a mathematics thes
 is that contributes to an understanding of\nnonlocal games as formal objec
 ts. With that said\, it does have\nconnections to quantum information theo
 ry and physical operational\ninterpretations.\n\nNonlocal games are intera
 ctive protocols modelling two players\nattempting to win a game\, by answe
 ring a pair of questions posed by\nthe referee\, who then checks whether t
 heir answers are correct. The\nplayers may have access to a shared quantum
  resource state and may use\na pre-arranged strategy. Upon receiving their
  questions\, they can\nmeasure this state\, subject to some separation con
 straints\, in order\nto select their answers. A famous example is the CHSH
  game of\n[Cla+69]\, where making use of shared quantum entanglement gives
  the\nplayers an advantage over using classical strategies.\n\nThis thesis
  contributes to two separate questions arising in the study\nof synchronou
 s nonlocal games: their algebraic properties\, and their\ngeneralization t
 o the quantum question-and-answer setting. Synchronous\ngames are those in
  which players must respond with the same answer\,\ngiven the same questio
 n.\n\nFirst\, we study a synchronous version of the linear constraint game
 \,\nwhere the players must attempt to convince the referee that they share
 \na solution to a system of linear equations over a finite field. We\ngive
  a correspondence between two different algebraic objects\nmodelling perfe
 ct strategies for this game\, showing one is isomorphic\nto a quotient of 
 the other. These objects are the game algebra of\n[OP16] and the solution 
 group of [CLS17]. We also demonstrate an\nequivalence of these linear syst
 em games to graph isomorphism games on\ngraphs parameterized by the linear
  system.\n\nSecond\, we extend nonlocal games to quantum games\, in the se
 nse that\nwe allow the questions and answers to be quantum states of a bip
 artite\nsystem. We do this by quantizing the rule function\, games\, strat
 egies\,\nand correlations using a graphical calculus for symmetric monoida
 l\ncategories applied to the category of finite dimensional Hilbert\nspace
 s. This approach follows the overall program of categorical\nquantum mecha
 nics. To this generalized setting of quantum games\, we\nextend definition
 s and results around synchronicity. We also introduce\nquantum versions of
  the classical graph homomorphism [MR16] and\nisomorphism [Ats+16] games\,
  where the question and answer spaces are\nthe vertex algebras of quantum 
 graphs\, and we show that quantum\nstrategies realizing perfect correlatio
 ns for these games correspond\nto morphisms between the underlying quantum
  graphs.\n\nMC 2009 or\nZoom: https://uwaterloo.zoom.us/j/92051331429?pwd
 =fl6rjZHC4X7itlJpaJaxwpfzJINQvG.1
DTSTAMP:20260502T041418Z
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