  Motivated by the Bose et al.-Matletto-Vedral (BMV) proposal for detecting
quantum superposition of spacetime geometries, we study a toy model of a
quantum entanglement generation between two spins (qubits) mediated by a
relativistic free scalar field. After time evolution, spin correlation is
generated through the interactions with the field. Because of the associated
particle creation into an open system, the quantum state of spins is partially
decohered. In this paper, we give a comprehensive study of the model based on
the closed-time path formalism, focussing on relativistic causality and quantum
mechanical complementarity. We calculate various quantities such as spin
correlations, entanglement entropies, mutual information and negativity, and
study their behaviors in various limiting situations. In particular, we
calculate the mutual information of the two spins and compare it with spin
correlation functions. We also discuss why no quantum entanglement can be
generated unless both spins are causally affected by one another while spin
correlations are generated.
