Strength and typicality of nonlocality in multisetting and multipartite Bell scenarios

In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell scenarios involving up to seven qubits. As a result, in the first part of this manuscript, we report statistical distributions of a quantity reciprocal to the critical visibility for various multipartite quantum states subjected to random measurements. The statistical relevance of different classes of multipartite tight Bell inequalities violated with random measurements is investigated. We also introduce the concept of typicality of quantum correlations for pure states as the probability to generate a nonlocal behavior with both random state and measurement. Although this typicality is slightly above 5.3% for two qubits, for a modest increase in the number of involved particles it quickly surpasses 99.99%.

Figure 1

Nonlocality strength distributions for the two-qubit GHZ state with various quantities of measurement settings for each qubit. Sample size: ${10}^9$ (per state).

Figure 2

Nonlocality strength distributions for the two-qubit generalized $\mathrm{GHZ}(\alpha$) state with $2\times 2$ (dashed) and $4\times 4$ (solid) measurement settings and with selected values of $\alpha$. Sample size: ${10}^9$ (per state).

Figure 3

Nonlocality strength distributions for four-qubit states. Sample size: ${10}^8$ (per state).

Figure 4

Unexpected behavior of nonlocality strength distributions close to $\mathcal{S}=0$ for the W states. Sample size: ${10}^8$ (per state).

Figure 5

Nonlocality strength distributions for special and random five-qubit states. Sample size: ${10}^7$ (per state).