Entanglement generation and decoherence in a two-qubit system mediated by relativistic quantum field

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, focusing 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. In some cases, its inequality relation improves the trade-off relation between the fringe visibility and the distinguishability (which-way information) by giving a stronger upper bound on the visibility. We also discuss why no quantum entanglement can be generated unless both spins are causally affected by one another while spin correlations are generated.