  Quantumness for a bipartite unsteerable quantum correlation is operationally
characterized by the notion of super-unsteerability. Super-unsteerability
refers to the requirement of a larger dimension of the random variable that the
steering party has to preshare with the party to be steered in the classical
simulation protocol to generate an unsteerable correlation than the local
Hilbert space dimension of the quantum states (reproducing the given
unsteerable correlation) at the steering party's side. In the present study,
this concept of super-unsteerability is generalized by defining the notion of
super-bi-unsteerability for tripartite correlations, which is unsteerable
across a bipartite cut. Genuine super-bi-unsteerability is defined as the
occurrence of super-bi-unsteerability across all possible bipartite cuts.
Specific example of genuine super-bi-unsteerability for tripartite correlations
has been presented. This study provides a tool to characterize the genuine
quantumness of tripartite quantum correlations which are unsteerable across
every bipartite cut.
