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URL:https://uwaterloo.ca/institute-for-quantum-computing/events/iqc-student
 -seminar-featuring-yuming-zhao
LOCATION:QNC - Quantum Nano Centre 200 University Avenue West QNC 1201 Wate
 rloo ON N2L 3G1 Canada
SUMMARY:IQC Student Seminar Featuring Yuming Zhao
CLASS:PUBLIC
DESCRIPTION:POSITIVITY AND SUM-OF-SQUARES IN QUANTUM INFORMATION\n\nA multi
 variate polynomial is said to be positive if it takes only\nnon-negative v
 alues over reals. Hilbert's 17th problem concerns\nwhether every positive 
 polynomial can be expressed as a sum of squares\nof other polynomials. In 
 general\, we say a noncommutative polynomial\nis positive (resp. matrix po
 sitive) if plugging operators (resp.\nmatrices) always yields a positive o
 perator. Many problems in math and\ncomputer science are closely connected
  to deciding whether a given\npolynomial is positive and finding certifica
 tes (e.g.\, sum-of-squares)\nof positivity.\n\nIn the study of nonlocal ga
 mes in quantum information\, we are\ninterested in tensor product of free 
 algebras. Such an algebra models\na physical system with two spatially sep
 arated subsystems\, where in\neach subsystem we can make different quantum
  measurements. The recent\nand remarkable MIP*=RE result shows that it is 
 undecidable to\ndetermine whether a polynomial in a tensor product of free
  algebras is\nmatrix positive. In this talk\, I'll present joint work with
  Arthur\nMehta and William Slofstra\, in which we show that it is undecida
 ble to\ndetermine positivity in tensor product of free algebras. As a\ncon
 sequence\, there is no sum-of-square certificate for positivity in\nsuch a
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DTSTAMP:20260407T030927Z
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