QLunch: Jurij Volcic

Speaker: Jurij Volcic from QMATH

Title: Sums-of-squares techniques in quantum information

Abstract: Sum-of-squares certificates of positivity play an important role in noncommutative polynomial optimization, and are being applied to various problems in quantum information.

The first part of the talk overviews some basic principles behind SOS certificates (noncommutative inequalities, Positivstellensätze, semidefinite programming) and well-known examples (such as violations of Bell inequalities via the NPA hierarchy), while the second part addresses more recent development in trace polynomial optimization.