Connection among entanglement, mixedness, and nonlocality in a dynamical context
Laura Mazzola, Bruno Bellomo, Rosario Lo Franco, Giuseppe Compagno · Physical Review A · 2010
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.