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Importance of considering independent and identically distributed (iid)scenario is well-established in quantum theory. From entanglement detection toentangled state transformation, this scenario is useful in many tasks.Nevertheless, here we focus on the limitation of iid scenario. For thispurpose, we consider the notion of nonlocality associated with local statediscrimination problems (LSDPs). Here, the term `nonlocality' denotes thedifference between the local and the global abilities of discriminating quantumstates. It is natural to consider LSDPs to study the aforesaid limitationbecause iid copies of quantum states are considered as resource in theseproblems. However, we first explore entanglement as resource in LSDPs where thestates are pure. Then, we generalize our findings considering mixed states. Inpresent 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 locallydiscriminated even if finite number of iid copies of the states are available.But local discrimination of these states can be done consuming quite lessresource when we consider entanglement-assisted LSDPs. This allows us tocompare the degrees of nonlocality associated with similar LSDPs within thesame Hilbert space. Thus, we report a hierarchy of nonlocality which cannot becaptured through iid scenario but it can be observed when entanglement is usedas resource in certain LSDPs. Moreover, the difference in nonlocality mayincrease with increasing dimension. Finally, we show an application of ourtheory in secure locking of information and its resource-efficient extraction.

Limitation of independent and identical distribution to capture the hierarchy of nonlocality