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Using a sample of $1.31 \times 10^{9}$ $J/\psi$ events collected with theBESIII detector at the BEPCII collider, we study the decays of $J/\psi\rightarrow K_S K_L$ and $K_S K_S$. The branching fraction of$J/\psi\rightarrowK_S K_L$ is determined to be ${\cal B}(J/\psi \rightarrow K_SK_L)=(1.93\pm0.01~(\rm{stat.})\pm0.05~(\rm{syst.}))\times10^{-4}$, whichsignificantly improves on previous measurements. No clear signal is observedfor the $J/\psi \rightarrow K_S K_S$ process, and the upper limit at the 95%confidence level for its branching fraction is determined to be ${\calB}(J/\psi \rightarrow K_S K_S)<1.4\times10^{-8}$, which improves on theprevious searches by two orders in magnitude and reaches the order of theEinstein-Podolsky-Rosen expectation.

Branching fraction measurement of $J/\psi \rightarrow K_S K_L$ and search for $J/\psi \rightarrow K_S K_S$