  Certain quantum states are well-known to be particularly fragile in the
presence of decoherence, as illustrated by Schrodinger's famous gedanken cat
experiment. It has been better appreciated more recently that quantum states
can be characterized in a hierarchy of quantum quantities such entanglement,
quantum correlations, and quantum coherence. It has been conjectured that each
of these quantities have various degrees of fragility in the presence of
decoherence. Here we experimentally confirm this conjecture by preparing
tripartite photonic states and subjecting them to controlled amounts of
dephasing. When the dephasing is applied to all the qubits, we find that the
entanglement is the most fragile quantity, followed by the quantum coherence,
then mutual information. This is in agreement with the widely held expectation
that multipartite quantum correlations are a highly fragile manifestation of
quantumness. We also perform dephasing on one out of the three qubits on star
and $ W \bar{W} $ states. Here the distribution of the correlations and
coherence in the state becomes more important in relation to the dephasing
location.
