Andries Steenkamp

Bounding the separable rank via polynomial optimization

  • Sander Gribling
  • Monique Laurent
  • Andries Steenkamp
    • Categories Convex and Nonsmooth Optimization, Global Optimization Tags , , , , ,

    We investigate questions related to the set $\mathcal{SEP}_d$ consisting of the linear maps $\rho$ acting on $\mathbb{C}^d\otimes \mathbb{C}^d$ that can be written as a convex combination of rank one matrices of the form $xx^*\otimes yy^*$. Such maps are known in quantum information theory as the separable bipartite states, while nonseparable states are called entangled. In … Read more

    Optimizing hypergraph-based polynomials modeling job-occupancy in queueing with redundancy scheduling

  • Daniel Brosch
  • Monique Laurent
  • Andries Steenkamp
    • Categories Constrained Nonlinear Optimization Tags , , ,

    We investigate two classes of multivariate polynomials with variables indexed by the edges of a uniform hypergraph and coefficients depending on certain patterns of union of edges. These polynomials arise naturally to model job-occupancy in some queuing problems with redundancy scheduling policy. The question, posed by Cardinaels, Borstand van Leeuwaarden (arXiv:2005.14566, 2020), is to decide … Read more