  The monogamy relations of entanglement are highly significant. However, they
involve only amounts of entanglement shared by different subsystems. Results on
monogamy relations between entanglement and other kinds of correlations, and
particularly classical correlations, are very scarce. Here we experimentally
observe a tradeoff relation between internal quantum nonseparability and
external total correlations in a photonic system and found that even purely
classical external correlations have a detrimental effect on internal
nonseparability. The nonseparability we consider, measured by the concurrence,
is between different degrees of freedom within the same photon, and the
external classical correlations, measured by the standard quantum mutual
information, are generated between the photons of a photon pair using the
time-bin method. Our observations show that to preserve the internal
entanglement in a system, it is necessary to maintain low external
correlations, including classical ones, between the system and its environment.
