quantum graph parameters

Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization

  • David de Laat
  • Monique Laurent
  • Sander Gribling
    • Categories Semi-definite Programming Tags , ,

    In this paper we study bipartite quantum correlations using techniques from tracial polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a bipartite correlation. This hierarchy converges to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a quantum … Read more

    Linear conic formulations for two-party correlations and values of nonlocal games

  • Jamie Sikora
  • Antonios Varvitsiotis
    • Categories Applications - Science and Engineering, Graphs and Matroids, Linear, Cone and Semidefinite Programming Tags , , , , ,

    In this work we study the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. We show that the sets of classical, quantum, no-signaling and unrestricted correlations can be expressed as projections of affine sections of appropriate convex cones. As a by-product, we identify … Read more

    On the closure of the completely positive semidefinite cone and linear approximations to quantum colorings

  • Sabine Burgdorf
  • Monique Laurent
  • Teresa Piovesan
    • Categories Linear, Cone and Semidefinite Programming, Polyhedra Tags , , , , , ,

    We investigate structural properties of the completely positive semidefinite cone, consisting of all the nxn symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size. This cone has been introduced to model quantum graph parameters as conic optimization problems. Recently it has also been used to characterize the set Q of … Read more

    Conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone

  • Monique Laurent
  • Teresa Piovesan
    • Categories Linear, Cone and Semidefinite Programming Tags , , , , ,

    We investigate the completely positive semidefinite cone $\mathcal{CS}_+^n$, a new matrix cone consisting of all $n\times n$ matrices that admit a Gram representation by positive semidefinite matrices (of any size). In particular we study relationships between this cone and the completely positive and doubly nonnegative cones, and between its dual cone and trace positive non-commutative … Read more