Inequivalent Quantum Resources from Multipartite State Discrimination

Any two orthogonal quantum states can be perfectly distinguished via local operations and classical communication (LOCC), yet whether all orthogonal multipartite pairs incur an identical operational cost remains an open question. Here, we address the resource consumption required for local state discrimination across multipartite pair of states. We demonstrate that distinct pairs of orthogonal multipartite maximally entangled states require unequal amounts of quantum resources to achieve local distinguishability. Extending our framework beyond individual pairs, we analyze larger sets of both locally distinguishable and indistinguishable multipartite orthogonal states, revealing a nontrivial hierarchy in their entanglement consumption. These results show that the resource cost of LOCC discrimination is state-dependent, providing insight into the fine-grained structure of multipartite nonlocality.