Gravitationally mediated entanglement of fermionic qubits: from static to dynamical limits

We employ the quantum Boltzmann equation to analyze the gravitationally generated entanglement between two remote qubits by considering two explicit microscopic models. A graviton propagator is employed as the mediator of the interactions, while the qubits are considered in a spatial superposition state. Such a setup, in the case of any entanglement generation, could potentially offer experimental evidence for the quantization of gravity. By treating the qubits as spin-1/2 particles in wave packets, we establish that the entanglement arises from forward scattering processes involving graviton exchanges. In our study, we consider both static and dynamical limits of the propagator and show that only in the dynamical limit such entangled states can be generated. We also show that for the microscopic model based on the fermion particles in the background of magnetic field, the amount of entanglement depends on the Larmor frequency of the qubits, rather than their masses. These effects are observed to diminish in both models as the wave packet size increases. Our findings sheds more light into the gravity mediated entanglement between two spin-1/2 particles.