  Nonlocality is a key feature of quantum theory and is reflected in the
violation of Bell inequalities for entangled systems. The experimental tests
beyond the electromagnetism and massless quanta are of great importance for
understanding the nonlocality in different quantum interactions. In this work,
we develop a generalized Clauser-Horne inequality pertaining especially to the
high energy physics processes, which is quantum mechanical intervene free. We
find, in the process of pseudoscalar quarkonium exclusive decay to entangled
$\Lambda\bar{\Lambda}$ pairs, the inequality could be violated and is
verifiable in high energy experiments, like BES III or BELLE II.
