Test of CPT Symmetry and Quantum Mechanics with Experimental data from CPLEAR

We use fits to recent published CPLEAR data on neutral kaon decays to $\pi^+\pi^-$ and $\pi e\nu$ to constrain the CPT--violation parameters appearing in a formulation of the neutral kaon system as an open quantum-mechanical system. The obtained upper limits of the CPT--violation parameters are approaching the range suggested by certain ideas concerning quantum gravity.