We address the problem of detecting bipartite Bell nonlocality whenever the only experimental information are the intensities produced in each run of the experiment by an unknown number of particles. We point out that this scenario naturally occurs in Bell experiments with parametric down-conversion when the crystal is pumped by strong pulses, in Bell tests with distant sources and in which particles suffer different delays during their flight, in Bell experiments using living cells as photo detectors, and in Bell experiments where the pairing information is physically removed. We show that, although Bell nonlocality decreases as the number of particles increases, if the parties can distinguish arbitrarily small differences of intensities and the visibility is larger than 0.98, then Bell nonlocality can still be experimentally detected with fluxes of up to 15 particles. We show that this prediction can be tested with current equipment in a Bell experiment where pairing information is physically removed, but requires the assumption of fair sampling.

We define an alternative way of quantifying nonlocality of states based on Bell nonlocality of behaviors, called the trace-weighted nonlocal volume. The construction is based on the nonlocal volume, a quantifier of nonlocality for states that counts the volume of the set of measurements that give rise to nonlocal behaviors when applied to this state, plus the trace distance, a quantifier of nonlocality for behaviors based on the distance between the behavior and the local set. The key difference from preceding candidates was the introduction of a quantifier of nonlocality to weight each contribution from behaviors in the nonlocal volume. We list some interesting properties of this quantifier and investigate the (2, 2, 2) and (2, 3, 2) scenarios. We show that the weak anomaly of nonlocality for the (2, 2, 3) scenario persists, but the local minimum for nonlocality with the trace-weighted nonlocal volume occurs in a different state as compared to the minimum for the nonweighted version, showing that the weak anomaly is not an intrinsic characteristic of the scenario, but is strongly dependent of the choice of quantifier.

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Correlation boxes are hypothetical systems capable of producing the maximal algebraic violation of Bell inequalities, beyond the quantum bound and without superluminal signaling. The fact that these systems show stronger correlations than those presented by maximally entangled quantum states has been regarded as a demonstration that the former are more nonlocal than the latter. By employing an alternative, consistent measure of nonlocality, we show that this conclusion is not necessarily true. In addition, we find a class of correlation boxes that are less nonlocal than the quantum singlet with respect to the Clauser-Horne-Shimony-Holt inequality, being, at the same time, more nonlocal with respect to the 3322 inequality.