  A scheme for characterizing entanglement using the statistical measure of
correlation given by the Pearson correlation coefficient (PCC) was recently
suggested that has remained unexplored beyond the qubit case. Towards the
application of this scheme for the high dimensional states, a key step has been
taken in a very recent work by experimentally determining PCC and analytically
relating it to Negativity for quantifying entanglement of the empirically
produced bipartite pure state of spatially correlated photonic qutrits.
Motivated by this work, we present here a comprehensive study of the efficacy
of such an entanglement characterizing scheme for a range of bipartite qutrit
states by considering suitable combinations of PCCs based on a limited number
of measurements. For this purpose, we investigate the issue of necessary and
sufficient certification together with quantification of entanglement for the
two-qutrit states comprising maximally entangled state mixed with white noise
and coloured noise in two different forms respectively. Further, by considering
these classes of states for d=4 and 5, extension of this PCC based approach for
higher dimensions d is discussed.
