Convergence of SDP hierarchies for polynomial optimization on the   hypersphere
  We show how to bound the accuracy of a family of semi-definite programming relaxations for the problem of polynomial optimization on the hypersphere. Our method is inspired by a set of results from quantum information known as quantum de Finetti theorems. In particular, we prove a de Finetti theorem for a special class of real symmetric matrices to establish the existence of approximate representing measures for moment matrix relaxations. 
Andrew C. Doherty and Stephanie Wehner
math.OC cs.DS math-ph math.MP quant-ph