The signal of ill-defined CPT weakening entanglement in the $B_d$ system

In the presence of quantum gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky-Rosen correlation of the neutral meson system by adding an Entanglement-weakening term of the wrong exchange symmetry, the $omega$-effect. In the current paper we identify how to probe the complex $omega$ in the entangled $B_d$-system using Flavour(f)-CP(g) eigenstate decay channels: the connection between the Intensities for the two time-ordered decays (f, g) and (g, f) is lost. Appropriate observables are constructed allowing independent experimental determinations of Re($omega$) and Im($omega$), disentangled from CPT violation in the evolution Hamiltonian Re($theta$) and Im($theta$). 2-$sigma$ tensions for both Re($theta$) and Im($omega$) are shown to be uncorrelated.