Relating an entanglement measure with statistical correlators for two-qudit mixed states using only a pair of complementary observables

We focus on characterising 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 observables opens up a potentially rich direction of study which is applicable for both distillable and bound entangled states.