Correlation has been widely used to facilitate various information retrieval methods such as query expansion, relevance feedback, document clustering, and multi-modal fusion. Especially, correlation and independence are important issues when fusing different modalities that influence a multi-modal information retrieval process. The basic idea of correlation is that an observable can help predict or enhance another observable. In quantum mechanics, quantum correlation, called entanglement, is a sort of correlation between the observables measured in atomic-size particles when these particles are not necessarily collected in ensembles. In this paper, we examine a multimodal fusion scenario that might be similar to that encountered in physics by firstly measuring two observables (i.e., text-based relevance and image-based relevance) of a multi-modal document without counting on an ensemble of multi-modal documents already labeled in terms of these two variables. Then, we investigate the existence of non-classical correlations between pairs of multi-modal documents. Despite there are some basic differences between entanglement and classical correlation encountered in the macroscopic world, we investigate the existence of this kind of non-classical correlation through the Bell inequality violation. Here, we experimentally test several novel association methods in a small-scale experiment. However, in the current experiment we did not find any violation of the Bell inequality. Finally, we present a series of interesting discussions, which may provide theoretical and empirical insights and inspirations for future development of this direction.