  This paper is dedicated to a detailed analysis and computation of quantum
states of causal fermion systems. The mathematical core is to compute integrals
over the unitary group asymptotically for a large dimension of the group, for
various integrands with a specific scaling behavior in this dimension. It is
shown that, in a well-defined limiting case, the localized refined pre-state is
positive and allows for the description of general entangled states.
