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Higher dimensional quantum systems (qudits) present a potentially moreefficient means, compared to qubits, for implementing various informationtheoretic tasks. One of the ubiquitous resources in such explorations isentanglement. Entanglement Monotones (EMs) are of key importance, particularlyfor assessing the efficacy of a given entangled state as a resource forinformation theoretic tasks. Till date, investigations towards determination ofEMs have focused on providing their tighter lower bounds. There is yet nogeneral scheme available for direct determination of the EMs. Consequently, anempirical determination of any EM has not yet been achieved for entangled quditstates. The present paper fills this gap, both theoretically as well asexperimentally. First, we derive analytical relations between statisticalcorrelation 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 ofconcept, we then experimentally measure MP, MI and PCC of two-qutrit purestates and determine their N and EOF using these derived relations. This is auseful addition to the experimenter's toolkit wherein by using a limited numberof measurements (in this case 1 set of measurements), one can directly measurethe EMs in a bipartite arbitrary dimensional system. We obtain the value of Nfor 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 oneentanglement monotone by the same limited number of measurements, we argue thatit can serve as a unique experimental platform for quantitatively comparing andcontrasting the operational implications of entanglement monotones as well asshowing their non-monotonicity for a given bipartire pure qudit state.

Direct determination of entanglement monotones for arbitrary dimensional  bipartite states using statistical correlators and one set of complementary  measurements