Nonclassicality of local bipartite correlations

Simulating quantum nonlocality and steering requires augmenting preshared randomness with nonvanishing communication cost. This prompts the question of how one may provide such an operational characterization for the quantumness of correlations due to even unentangled states. Here we show that for a certain class of states, such quantumness can be pointed out by superlocality, the requirement for a larger dimension of the preshared randomness to simulate the correlations than that of the quantum state that generates them. This provides an approach to define the nonclassicality of local multipartite correlations in convex operational theories.

Figure 1

Bell–Clauser-Horne-Shimony-Holt two-input–two-out-put scenario appropriate for the correlations considered here, where $x$ and $y$ are Alice's and Bob's inputs, respectively; $a$ and $b$ are their outputs; and $x,y,a,b\in \{0,1\}$. Local quantum state $\rho$ is shared between them, giving rise to probability $P\left(ab\right|xy)$. The simulability of this probability by pre-sharing classical variable $\lambda$ of bounded dimension is considered here.

Figure 2

A section of the correlations that appear in the scenario of Fig. 1. The region NS within the outer square, bounded by PR boxes PR1, PR2, etc., represents nonsignaling correlations, with the quantum realizable ones given by the circular region Q, a subset of which is the local polytope L. The center C corresponds to the white-noise box. For each dashed diagonal line radiating from C towards a PR box but excluding C, the segment within Q represents a family of quantum boxes having the form of noisy PR boxes, which are superlocal even within L.