Quantifying quantum correlations beyond entanglement via robust photon hopping in an optomechanical system

Quantum correlations beyond quantum entanglement represent vital resources in quantum information processing as well as in quantum computation. In fact, both quantum entanglement and quantum correlation are the same when the quantum system is described by pure states. However, this is not exactly the case when general mixed states are considered. In order to clarify this, a simple model has been proposed for the production and quantification of these quantum correlations between two mechanical resonators that are macroscopic in two Fabry-Perot cavities optomechanical coupled by the photon hopping process. In this model, we analyze and investigate the quantification of the quantum correlation beyond the entanglement between the mechanical modes. We determine the global covariance matrix of the model from which we derive the expression of the entropy of formation (Ef) as well as the Gaussian quantum discord (GD), which quantify the amount of quantum entanglement and quantum correlations, respectively. The analysis based on these two quantum correlations quantifiers shows that quantum discord is more appropriate to characterize the quantum correlations between the mechanical modes in an optomechanical quantum system in the presence of robust photon hopping.