Are There Phase Transitions in Information Space?

The interplay between two basic quantities—quantum communication and information—is investigated. Quantum communication is an important resource for quantum states shared by two parties and is directly related to entanglement. Recently, the amount of local information that can be drawn from a state has been shown to be closely related to the nonlocal properties of the state. Here we consider both formation and extraction processes, and analyze informational resources as a function of quantum communication. The resulting diagrams in information space allow us to observe phaselike transitions when correlations become classical.

Figure 1

Formation and extraction curves for a generic mixed state. The short-dashed line represents the variant where information can be extracted from the “garbage” left after entanglement distillation ($I_g>0$). In general, the curves need not be smooth. The formation curve is in the lower left quadrant.

Figure 2

(a) Pure states, (b) states with $\Delta =0$, (c) separable states with $\Delta >0$, and (d) bound entangled states with $\Delta >0$.

Figure 3

“Phase transition” in the family of states of Eq. (7).