  Optically coupled optomechanical oscillators has turned out to be a versatile
experimental resource for exploring optomechanical synchronizations and
correlations. In this work, we investigate the phenomena of quantum
synchronization and quantum correlations in two optically coupled
optomechanical oscillators with two different topologies. In one case the
oscillators are coupled with optical photons in a reversible manner, termed as
bidirectional coupling, while in the other photons are allowed to enter to the
other oscillator but not allowed to exchanged back in the opposite direction,
termed as unidirectional coupling. Our results shows that irrespective of these
configurations, when synchronization builds up, the two oscillators also become
quantum mechanically correlated with a finite degree of Gaussian quantum
discord. However, we find that depending on these topologies, both
synchronization and quantum discord behave in a very distinctive manner. For
instance, in bidirectionally coupled optomechanical oscillators, we find both
quantum synchronization and discord exhibit a tongue like pattern which is the
quantum analogue of an Arnold tongue. Whereas, in the unidirectionally coupled
oscillators, we observe a novel blockade like behavior for quantum phase
synchronization, also known as the quantum synchronization blockade, while
quantum discord being failed to map such an anomalous behavior.
