Abstract
The Einstein-Podolsky-Rosen~(EPR) model is an analogous model of the anti-ferromagnetic Heisenberg model or the equivalent quantum maximum-cut problem, proposed by R. King two years ago. Adjacent qubits in the model prefer symmetric EPR/Bell parings rather than the antisymmetric one, in order to maximize the energy. Recently, two groups independently develop specific algorithms for the highest-energy state with approximation ratio 1+√5/4≈.809, based on maximum fractional matchings. Here we try to refine one of the two algorithms by devising homogeneous/quasi-homogeneous fractional matchings, with the aim to distribute quantum entanglement as much as possible. For regular graphs G_d, we immediately obtain increasing approximation ratios r_d with r₂=3+√5/6≈.872. For irregular graphs, we show such a refinement could still guarantee nice performance if the fractional matchings are chosen properly.