Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization
本文用迹非交换多项式优化技术研究二分量子关联的优化问题，构造了半定规划下界来估计最小平均纠缠维数，并统一了量子色数和量子稳定数的现有界。
In this paper we study optimization problems related to bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. First we consider the problem of finding the minimal entanglement dimension of such correlations. We construct a hierarchy of semidefinite programming lower bounds and show convergence to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a quantum correlation when access to shared randomness is free. Then we study optimization problems over synchronous quantum correlations arising from quantum graph parameters. We introduce semidefinite programming hierarchies and unify existing bounds on quantum chromatic and quantum stability numbers by placing them in the framework of tracial polynomial optimization.