2015/07/27 by Miguel Navascues, Adrien Feix, Mateus Araujo +1 · 1 citation
Physics and Astronomy · Mathematics · #quant-ph #math.OC
paper · pdf · doi:10.1103/physreva.92.042117
published as Phys. Rev. A 92, 042117 (2015) · 17 pages
arxiv created 2015/07/27 · arxiv updated 2015/10/28
We study and extend the semidefinite programming (SDP) hierarchies introduced in [Phys. Rev. Lett. 115, 020501] for the characterization of the statistical correlations arising from finite dimensional quantum systems. First, we introduce the dimension-constrained noncommutative polynomial optimization (NPO) paradigm, where a number of polynomial inequalities are defined and optimization is conducted over all feasible operator representations of bounded dimensionality. Important problems in device independent and semi-device independent quantum information science can be formulated (or almost formulated) in this framework. We present effective SDP hierarchies to attack the general dimension-constrained NPO problem (and related ones) and prove their asymptotic convergence. To illustrate the power of these relaxations, we use them to derive new dimension witnesses for temporal and Bell-type correlation scenarios, and also to bound the probability of success of quantum random access codes.