  Importance of considering independent and identically distributed (iid)
scenario is well-established in quantum theory. From entanglement detection to
entangled state transformation, this scenario is useful in many tasks.
Nevertheless, here we focus on the limitation of iid scenario. For this
purpose, we consider the notion of nonlocality associated with local state
discrimination problems (LSDPs). Here, the term `nonlocality' denotes the
difference between the local and the global abilities of discriminating quantum
states. It is natural to consider LSDPs to study the aforesaid limitation
because iid copies of quantum states are considered as resource in these
problems. However, we first explore entanglement as resource in LSDPs where the
states are pure. Then, we generalize our findings considering mixed states. In
present LSDPs, our findings make the teleportation-based protocols sub-optimal.
In fact, our results shed light on Schmidt rank as resource in LSDPs.
Interestingly, we find instances where the states cannot be locally
discriminated even if finite number of iid copies of the states are available.
But local discrimination of these states can be done consuming quite less
resource when we consider entanglement-assisted LSDPs. This allows us to
compare the degrees of nonlocality associated with similar LSDPs within the
same Hilbert space. Thus, we report a hierarchy of nonlocality which cannot be
captured through iid scenario but it can be observed when entanglement is used
as resource in certain LSDPs. Moreover, the difference in nonlocality may
increase with increasing dimension. Finally, we show an application of our
theory in secure locking of information and its resource-efficient extraction.
