We show that correlations between observables on composite quantum systems can be mathematically represented as correlations of quadratic forms of classical Gaussian signals. The formalism covers correlations for entangled quantum systems; for example, measurements of spin projections for two electrons in the singlet state. In this paper we show that at the subquantum level all quantum systems are correlated including systems in factorizable states. However, in the latter case quadratic forms of the prequantum fields (at the subquantum level these forms represent quantum observables) are uncorrelated. Thus “subquantum entanglement” for prequantum fields representing quantum systems in factorizable states cannot be found by using quantum observables. We have to go beyond quantum mechanics. Coupling with generalized quantum models of Mielnik and Zyczkowski are discussed.