2013/12/23 by Monique Laurent, Laurent, Monique, Teresa Piovesan +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Optimization and Control (math.OC) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math.OA #math.OC #quant-ph
paper · pdf · doi:10.48550/arxiv.1312.6643
Fixed some typos
openalex publication_date 2013/12/23 · arxiv created 2015/10/05 · arxiv updated 2015/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the completely positive semidefinite cone CS+n, a new matrix cone consisting of all n× 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 polynomials. We use this new cone to model quantum analogues of the classical independence and chromatic graph parameters α(G) and χ(G), which are roughly obtained by allowing variables to be positive semidefinite matrices instead of 0/1 scalars in the programs defining the classical parameters. We can formulate these quantum parameters as conic linear programs over the cone CS+n. Using this conic approach we can recover the bounds in terms of the theta number and define further approximations by exploiting the link to trace positive polynomials.