BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Drupal iCal API//EN X-WR-CALNAME:Events items teaser X-WR-TIMEZONE:America/Toronto BEGIN:VTIMEZONE TZID:America/Toronto X-LIC-LOCATION:America/Toronto BEGIN:DAYLIGHT TZNAME:EDT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 DTSTART:20230312T070000 END:DAYLIGHT BEGIN:STANDARD TZNAME:EST TZOFFSETFROM:-0400 TZOFFSETTO:-0500 DTSTART:20221106T060000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:6569488b45f3d DTSTART;TZID=America/Toronto:20230809T120000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20230809T130000 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.]  Google\n[ event/ul18248865+google]  Office 365\n[ 18248865+office365]  Outlook\n[ +outlook]\n[ okcom]  Yahoo\n[]  \n DTSTAMP:20231201T024427Z END:VEVENT END:VCALENDAR