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Chained correlation inequalities involving pairwise correlations of qubitobservables in the equatorial plane are constructed based on the positivity ofa sequence of moment matrices. When a jointly measurable set of fuzzy POVMs isemployed in first measurement of every pair of sequential measurements, thechained pairwise correlations do not violate the classical bound imposed by themoment matrix positivity. We identify that incompatibility of measurements isonly necessary, but not sufficient, in general, for the violation of theinequality. On the other hand, there exists a one-to-one equivalence betweenthe degree of incompatibility (which quantifies the joint measurability) of theequatorial qubit observables and the optimal violation of a non-local steeringinequality, proposed by Jones and Wiseman (Phys. Rev. A, 84, 012110 (2011)). Tothis end, we construct a local analogue of this steering inequality in a singlequbit system and show that its violation is a mere reflection of measurementincompatibility of equatorial qubit POVMs, employed in first measurements inthe sequential unsharp-sharp scheme.

N term pairwise correlation inequalities, steering and joint measurability