Probing bath-induced entanglement in a qubit pair by measuring photon correlations

Self-assembled quantum dots (QDs) are ideal structures in which to test theories of open quantum systems: confined exciton states can be coherently manipulated and their decoherence properties are dominated by interactions with acoustic phonons. We here describe the interaction of a pair of un-coupled, driven, QD excitons with a common phonon environment, and find that this coupling effectively generates two kinds of interaction between the two QDs: an elastic coupling mediated by virtual phonons and an inelastic coupling mediated by real phonons. We show that both of these interactions produce steady state entanglement between the two QD excitons. We also show that photon correlations in the emission of the QDs can provide a signature of the common environment. Experiments to demonstrate our predictions are feasible with the state-of-the-art technology and would provide valuable insight into QD carrier-phonon dynamics.