Connection among entanglement, mixedness and nonlocality in a dynamical context

We investigate the dynamical relations among entanglement, mixedness, and nonlocality, quantified by concurrence C, purity P, and maximum Bell function B, respectively, in a system of two qubits in a common structured reservoir. To this aim we introduce the C-P-B parameter space and analyze the time evolution of the point representative of the system state in such a space. The dynamical interplay among entanglement, mixedness, and nonlocality strongly depends on the initial state of the system. For a two-excitation Bell state the representative point draws a multibranch curve in the C-P-B space and we show that a closed relation among these quantifiers does not hold. By extending the known relation between C and B for pure states, we give an expression among the three quantifiers for mixed states. In this equation we introduce a quantity, vanishing for pure states, which in general does not have a closed form in terms of C, P and B. Finally, we demonstrate that for an initial one-excitation Bell state, a closed C-P-B relation instead exists and the system evolves, remaining always a maximally entangled mixed state.