completely positive semidefinite cone

Completely positive semidefinite rank

  • Anupam Prakash
  • Jamie Sikora
  • Antonios Varvitsiotis
  • Zhaohui Wei
    • Categories Linear, Cone and Semidefinite Programming Tags , , , , , , ,

    An $n\times n$ matrix $X$ is called completely positive semidefinite (cpsd) if there exist $d\times d$ Hermitian positive semidefinite {matrices} $\{P_i\}_{i=1}^n$ (for some $d\ge 1$) such that $X_{ij}= {\rm Tr}(P_iP_j),$ for all $i,j \in \{ 1, \ldots, n \}$. The cpsd-rank of a cpsd matrix is the smallest $d\ge 1$ for which such a representation … 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