Roughness as Entanglement Witness: The two Coupled Cavity Model

In this work we investigate the entanglement dynamics of two coupled superconducting cavities, whose excitation levels can be 0 or 1, thus representing the implementation of a two qubit system. We use the Concurrence as a measure of entanglement between the two systems and compare it to the Roughness of the system, which indicates the degree of classicality of a given quantum state. Although the Concurrence values are not directly related with the Roughness of each subsystem alone, we found evidence of correlation between the two functions when considering a generalized sum of Roughness over the two subsystems, whereas the minimum of one of them occurs for the maximum of the other. Based on the behavior of the two functions, we use them to propose a new Quantum Resource Quantifier.