The signal of ill-defined CPT weakening entanglement in the [Formula: see text] 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 [Formula: see text] -effect. In the current paper we identify how to probe the complex [Formula: see text] in the entangled [Formula: see text] -system using the 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([Formula: see text] ) and Im([Formula: see text] ), disentangled from CPT violation in the evolution Hamiltonian Re([Formula: see text] ) and Im([Formula: see text] ). [Formula: see text] tensions for both Re([Formula: see text] ) and Im([Formula: see text] ) are shown to be uncorrelated.