  Higher dimensional quantum systems (qudits) present a potentially more
efficient means, compared to qubits, for implementing various information
theoretic tasks. One of the ubiquitous resources in such explorations is
entanglement. Entanglement Monotones (EMs) are of key importance, particularly
for assessing the efficacy of a given entangled state as a resource for
information theoretic tasks. Till date, investigations towards determination of
EMs have focused on providing their tighter lower bounds. There is yet no
general scheme available for direct determination of the EMs. Consequently, an
empirical determination of any EM has not yet been achieved for entangled qudit
states. The present paper fills this gap, both theoretically as well as
experimentally. First, we derive analytical relations between statistical
correlation measures i.e. Mutual Predictability (MP), Mutual Information (MI)
and Pearson Correlation Coefficient (PCC) and standard EMs i.e. Negativity (N)
and Entanglement of Formation (EOF) in arbitrary dimensions. As a proof of
concept, we then experimentally measure MP, MI and PCC of two-qutrit pure
states and determine their N and EOF using these derived relations. This is a
useful addition to the experimenter's toolkit wherein by using a limited number
of measurements (in this case 1 set of measurements), one can directly measure
the EMs in a bipartite arbitrary dimensional system. We obtain the value of N
for our bipartite qutrit to be 0.907 $\pm$ 0.013 and the EOF to be 1.323 $\pm$
0.022. Since the present scheme enables determination of more than one
entanglement monotone by the same limited number of measurements, we argue that
it can serve as a unique experimental platform for quantitatively comparing and
contrasting the operational implications of entanglement monotones as well as
showing their non-monotonicity for a given bipartire pure qudit state.
