Tripartite quantum state violating the hidden-influence constraints

The possibility to explain quantum correlations via (possibly) unknown causal influences propagating gradually and continuously at a finite speed $v>c$ has attracted some attention recently. In particular, it could be shown that this assumption leads to correlations that can be exploited for superluminal communication. This was achieved studying the set of possible correlations that are allowed within such a model and comparing them to correlations produced by local measurements on a four-party entangled quantum state. Here, we report on a quantum state that allows for the same conclusion involving only three parties.

Figure 1

Space-time diagram in the preferred reference frame illustrating the concepts of $v$-connected and $v$-disconnected events. The shaded regions are the $c$ cones (light cones) and the striped regions show the $v$ cones with $v>c$. The $v$ cones of $K_1$ contain all points that can reach $K_1$, or that can be reached from $K_1$, by signals (influences) propagating at a speed not larger than $v$.

Figure 2

Space-time diagrams showing the two relevant time orderings for the tripartite scenario. Here, $A$ and $C$ are simultaneous in the hypothetical preferred frame of reference. In (b), the common past $v$ cones of $A$ and $C$ also include $B$, labeled by input $y$ and output $b$.

Figure 3

The space-time configuration to demonstrate superluminal communication for correlations $P\left(ac\right|xz,by)$ that depend on $y$ and $b$. The solid lines represent the $c$ cones and the dashed lines the $v$ cones, respectively.