We give an efficient 0.8395-approximation algorithm for the EPR Hamiltonian. Our improvement comes from a new nonlinear monogamy-of-entanglement bound on star graphs and a refined parameterization of a shallow quantum circuit from previous works. We also prove limitations showing that current methods cannot achieve substantially better approximation ratios, indicating that further progress will require fundamentally new techniques.

翻译：我们针对EPR哈密顿量提出了一种高效的0.8395近似算法。该改进源于星图纠缠单调性的新型非线性约束，以及对先前工作中浅层量子电路参数的精细化重构。我们同时证明了现有方法无法获得显著更优近似比的理论局限，表明进一步突破需要本质性的创新技术。