  The notion of incompatibility of measurements in quantum theory is in stark
contrast with the corresponding classical perspective, where all physical
observables are jointly measurable. It is of interest to examine if the results
of two or more measurements in the quantum scenario can be perceived from a
classical point of view or they still exhibit non-classical features. Clearly,
commuting observables can be measured jointly using projective measurements and
their statistical outcomes can be discerned classically. However, such simple
minded association of compatibility of measurements with commutativity turns
out to be limited in an extended framework, where the usual notion of sharp
projective valued measurements of self adjoint observables gets broadened to
include unsharp measurements of generalized observables constituting positive
operator valued measures (POVM). There is a surge of research activity recently
towards gaining new physical insights on the emergence of classical behavior
via joint measurability of unsharp observables. Here, we explore the entropic
uncertainty relation for a pair of discrete observables (of Alice's system)
when an entangled quantum memory of Bob is restricted to record outcomes of
jointly measurable POVMs only. Within the joint measurability regime, the sum
of entropies associated with Alice's measurement outcomes - conditioned by the
results registered at Bob's end - are constrained to obey an entropic steering
inequality. In this case, Bob's non-steerability reflects itself as his
inability in predicting the outcomes of Alice's pair of non-commuting
observables with better precision, even when they share an entangled state. As
a further consequence, the quantum advantage envisaged for the construction of
security proofs in key distribution is lost, when Bob's measurements are
restricted to the joint measurability regime.
