  We analyze the quantum-to-classical transition (QCT) for coupled bipartite
quantum systems for which the position of one of the two subsystems is
continuously monitored. We obtain the surprising result that the QCT can emerge
concomitantly with the presence of highly entangled states in the bipartite
system. Furthermore the changing degree of entanglement is associated with the
back-action of the measurement on the system and is itself an indicator of the
QCT. Our analysis elucidates the role of entanglement in von Neumann's paradigm
of quantum measurements comprised of a system and a monitored measurement
apparatus.
