The explosive development of quantum magnonics is explained by its potential of use in quantum computers, processing information and the formation of hybrid quantum systems. The processes of spatial correlation of quantum systems are fundamental and lead to such phenomena as the Josephson effect and superconductivity. In particular, they determine the phenomenon of the magnon superfluidity and magnon Bose condensation which were first discovered in antiferromagnetic superfluid 3He. In this article, we consider the features of magnon Bose condensation in yttrium iron garnet film. We simulate the processes of magnon BEC coherency and magnon tunneling through the gap.