Bound Nonlocality and Activation

We investigate nonlocality distillation using measures of nonlocality based on the Elitzur-Popescu-Rohrlich decomposition. For a certain number of copies of a given nonlocal box, we define two quantities of interest: (i) the nonlocal cost and (ii) the distillable nonlocality. We find that there exist boxes whose distillable nonlocality is strictly smaller than their nonlocal cost. Thus nonlocality displays a form of irreversibility which we term “bound nonlocality.” Finally, we show that nonlocal distillability can be activated.

Figure 1

Section of the no-signaling polytope given by nonlocal boxes $P(\xi ,\gamma )$. The region features three qualitatively different types of boxes: (I) two-copy distillable boxes, (II) two-copy bound nonlocal boxes, and (III) HH boxes. Inset: Contour plot of the nonlocal cost of two copies, showing lines of constant $C[P^{\times 2}(\xi ,\gamma )]$.