  Spontaneous synchronization is a fundamental phenomenon, important in many
theoretical studies and applications. Recently this effect has been analyzed
and observed in a number of physical systems close to the quantum mechanical
regime. In this work we propose the mutual information as a useful order
parameter which can capture the emergence of synchronization in very different
contexts, ranging from semi-classical to intrinsically quantum mechanical
systems. Specifically we first study the synchronization of two coupled Van der
Pol oscillators in both classical and quantum regimes and later we consider the
synchronization of two qubits inside two coupled optical cavities. In all these
contexts, we find that mutual information can be used as an appropriate figure
of merit for determining the synchronization phases, independently of the
specific details of the system.
