Detection of nonlocal superpositions

We study in theory and experiment the verification of the Schmidt number of quantum correlated radiation fields. This measure of entanglement counts the number of global superpositions of product states which are needed to describe a compound quantum system. For unraveling a certain value of this measure, a family of entanglement and Schmidt number tests is constructed. The measurement of the whole class of witnesses is realized. By generating a path entangled two-photon state, we demonstrate the feasibility to directly count quantum superpositions.