Emergence of Quantum Correlations from Nonlocality Swapping

By studying generalized nonsignaling theories, the hope is to find out what makes quantum mechanics so special. In the present Letter, we revisit the paradigmatic model of nonsignaling boxes and introduce the concept of a genuine box. This will allow us to present the first generalized nonsignaling model featuring quantumlike dynamics. In particular, we present the coupler, a device enabling nonlocality swapping, the analogue of quantum entanglement swapping, as well as teleportation. Remarkably, part of the boundary between quantum and post-quantum correlations emerges in our study.

Figure 1

The set of allowed states is restricted to (i) the local polytope $\mathcal{L}$ and (ii) the PR box. The other PR boxes are discarded since they are not genuine and should therefore not be considered for nonlocality swapping. The left axis is the CH value. Local states satisfy $0\le \overrightarrow{\mathrm{CH}}·{\overrightarrow{P}}^L\le 1$, the CH Bell inequality. The coupler (right axis) is a rescaling of the CH value (see text). Note that the polytope is eight-dimensional; the figure is a two-dimensional illustration.

Figure 2

Genuine boxes. (a) A “quantum” black box contains a quantum state and measurement devices (polarizers and detectors). The orientation of the polarizers depends on the input values $x$ and $y$. The genuine part of the box is the quantum state; before performing a joint measurement, one must remove the measurement devices. (b) A nongenuine PR box contains the genuine PR box and classical circuitry. Importantly, upon applying the coupler, one should first open the box, remove the circuitry, and connect the coupler directly to the genuine PR box.

Figure 3

(a) Entanglement swapping and (b) nonlocality swapping. The coupler is the analogue of the quantum joint measurement.

Figure 4

In a whole section of the polytope, the boxes useless for nonlocality swapping correspond exactly to the set of quantum boxes $\mathcal{Q}$ (red region), characterized by the TLM criteria; for isotropic boxes (dashed line), this corresponds to Tsirelson’s bound (cross) $B_Q=\frac{1}{\sqrt{2}}+\frac{1}{2}$, the quantum bound of the CH inequality.