  We focus on characterizing entanglement of high dimensional bipartite states
using various statistical correlators for two-qudit mixed states. The salient
results obtained are as follows: (a) A scheme for determining the entanglement
measure given by Negativity is explored by analytically relating it to the
widely used statistical correlators viz. mutual predictability, mutual
information and Pearson Correlation coefficient for different types of
bipartite arbitrary dimensional mixed states. Importantly, this is demonstrated
using only a pair of complementary observables pertaining to the mutually
unbiased bases. (b) The relations thus derived provide the separability bounds
for detecting entanglement obtained for a fixed choice of the complementary
observables, while the bounds per se are state-dependent. Such bounds are
compared with the earlier suggested separability bounds. (c) We also show how
these statistical correlators can enable distinguishing between the separable,
distillable and bound entanglement domains of the one-parameter Horodecki
two-qutrit states. Further, the relations linking Negativity with the
statistical correlators have been derived for such Horodecki states in the
domain of distillable entanglement. Thus, this entanglement characterisation
scheme based on statistical correlators and harnessing complementarity of the
obsevables opens up a potentially rich direction of study which is applicable
for both distillable and bound entangled states.
