Test of quantum nonlocality via vector meson decays to $K_SK_S$

In the system of a pair of quantum-entangled neutral kaons from meson decays, when one kaon collapses into the $K_S$ state, the other will collapse instantaneously into the $K_L$ state due to entanglement and nonlocality. However, if the alternative hypothesis is correct and there's a time window during which one kaon is unaware that the other has decayed, some quantum mechanically prohibited $K_SK_S$ decays may occur. We calculate the branching ratios of $K_SK_S$ in vector meson decays under the locality hypothesis and compare them with experimental results. We show that the branching ratio of $J/\psi\rightarrow K_SK_S$ under locality assumption is already excluded by the BESIII experimental upper limit. Additional experimental results are proposed to perform this test in the future.