Correlations in local measurements and entanglement in many-body systems

While entanglement plays an important role in characterizing quantum many-body systems, it is hardly possible to directly access many-body entanglement in real experiments. In this paper, we study how bipartite entanglement of many-body states is manifested in the correlation of local measurement outcomes. In particular, we consider a measure of correlation defined as the statistical distance between the joint probability distribution of local measurement outcomes and the product of its marginal distributions. Various bounds of this measure are obtained and several examples of many-body states are considered as a testbed for the measure. We also generalize the framework to the case of imprecise measurement and argue that the considered measure is related to the concept of quantum macroscopicity.