  Superlocality and superunsteerability provide operational characterization of
quantum correlations in certain local and unsteerable states respectively. Such
quantum correlated states have a nonzero quantum discord. A two-way nonzero
quantum discord is necessary for quantum correlations pointed out by
superlocality. On the other hand, in this work, we demonstrate that a two-way
nonzero quantum discord is not necessary to demonstrate superunsteerability. To
this end, we demonstrate superunsteerability for one-way quantum discordant
states. This in turn implies the existence of one-way superunsteerability and
also the presence of superunsteerability without superlocality.
Superunsteerability for nonzero quantum discord states implies the occurence of
steerability in a one-sided semi-device-independent way. Just like one-way
steerability occurs for certain Bell-local states in a one-sided
device-independent way, our result shows that one-way steerability can also
occur for certain nonsuperlocal states but in a one-sided
semi-device-independent way.
