Strength and typicality of nonlocality in multisetting and multipartite Bell scenarios

Abstract

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 7 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 behaviour with both random state and measurement. Although this typicality is slightly above 5.3% for the CHSH scenario, for a modest increase in the number of involved qubits it quickly surpasses 99.99%.

Experimentally friendly approach towards nonlocal correlations in multisetting N-partite Bell scenarios

“…the multipartite entangled states may reveal nonlocal correlations between any pair of qubits, in contrast to the biseparable state |ψ . Finally, a very interesting observation can be made when comparing our results with the previous calculations based on linear programming method [15,20]. As illustrated in Fig.…”

“…However, the value of m 3 and m 4 undoubtedly influences the resulting nonlocal strength (see Table 3). Furthermore, the average S of |ψ is around two times greater than that of |GHZ 2 [20]. For instance,S 2×2×1×1 (ψ) = 0.0536 whileS 2×2 (GHZ 2 ) = 0.028.…”

“…Following this observation, a new quantity called nonlocality strength, S, can be defined [20]. It is given by S = 1 − v crit .…”

“…the number of settings determines the number of two-qubit state achieved after single-qubit projections and so, it becomes more likely that at least one of these states violates the CHSH inequality. Furthermore, except the simplest scenario, [20].…”

“…(1) fairly captures the nonlocality extent of a state, the nonlocal fraction does not provide much information about the strength of nonlocality. Therefore, it seems useful to put it together with another quantitative description, called nonlocality strength, which addresses the "fragility" of this nonlocality against noise [20].…”