Quantum Gravity may be entirely unconventional as a theory, leading to completely unfamiliar (compared to other fields of physics) and unexpected experimental signatures. One particularly interesting avenue for research in that field is the study of models in which quantum gravity operates as a decoherening ``foamy space-time medium\'\', with which ordinary propagating matter interacts. In such theories, which appear to involve the evolution of pure quantum mechanical states to mixed ones, at an effective low-energy level, the CPT operator of the effective low-energy field theory is ill defined, at least in its strong form, as argued in a theorem by R. Wald (1980) . This induces ``Microscopic Time Irreversibility\'\', a fundamental ``arrow of time\'\' in the effective theory. Experimentally of course, this arrow may not be observable: one may face a situation in which the experimentally accessible subspaces of quantum-mechanical states are decoherence-free subspaces, such that the relevant observables appear to be CPT symmetric, despite the strong form of CPT violation. This can happen, for instance, if cancellations of the ``anomalous\'\' CPT Violating terms between particle and antiparticle sectors occur. However, there are concrete quantum-gravity models of space time foam (some within the context of (non-critical) string theory), in which there are clear, and possibly unique (``smoking-gun\'\' type), experimental signatures of such an intrinsic CPT violation, manifesting themselves in induced modifications of the Einstein-Podolsky-Rosen (EPR) correlations of entangled states of neutral mesons in the appropriate meson factories. In the talk I will review the situation in some detail, discussing some indicative estimates of the effect, within some specific (non-critical) string models of space time foam for concreteness, as well as outlining the current experimental limits in phi- and B-meson factories and prospects for improvement in upcoming meson facilities, such as a possible upgrade of DaPhiNe. As I will argue, some models of this type of intrinsic CPT Violation may be falsified in such upgraded facilities.