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DTSTART:20230312T070000
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DTSTART;TZID=America/Toronto:20230809T120000
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SUMMARY:IQC Student Seminar Featuring Yuming Zhao
CLASS:PUBLIC
DESCRIPTION:Summary \n\nPOSITIVITY AND SUM-OF-SQUARES IN QUANTUM INFORMATIO
 N\n\nA multivariate polynomial is said to be positive if it takes only\nno
 n-negative values over reals. Hilbert's 17th problem concerns\nwhether eve
 ry positive polynomial can be expressed as a sum of squares\nof other poly
 nomials. In general\, we say a noncommutative polynomial\nis positive (res
 p. matrix positive) if plugging operators (resp.\nmatrices) always yields 
 a positive operator. Many problems in math and\ncomputer science are close
 ly connected to deciding whether a given\npolynomial is positive and findi
 ng certificates (e.g.\, sum-of-squares)\nof positivity.\n\nIn the study of
  nonlocal games in quantum information\, we are\ninterested in tensor prod
 uct of free algebras. Such an algebra models\na physical system with two s
 patially separated subsystems\, where in\neach subsystem we can make diffe
 rent quantum measurements. The recent\nand remarkable MIP*=RE result shows
  that it is undecidable to\ndetermine whether a polynomial in a tensor pro
 duct of free algebras is\nmatrix positive. In this talk\, I'll present joi
 nt work with Arthur\nMehta and William Slofstra\, in which we show that it
  is undecidable to\ndetermine positivity in tensor product of free algebra
 s. As a\nconsequence\, there is no sum-of-square certificate for positivit
 y in\nsuch algebras.\n\n \n\nADD EVENT TO CALENDAR\n\nApple [https://www.
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DTSTAMP:20231201T024427Z
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