  Discrimination of quantum states under local operations and classical
communication (LOCC) is an intriguing question in the context of local
retrieval of classical information, encoded in the multipartite quantum
systems. All the local quantum state discrimination premises, considered so
far, mimic a basic communication set-up, where the spatially separated decoding
devices are independent of any additional input. Here, exploring a generalized
communication scenario we introduce a framework for input-dependent local
quantum state discrimination, which we call local random authentication (LRA).
Referring to the term nonlocality, often used to indicate the impossibility of
local state discrimination, we coin the term conditional nonlocality for the
impossibility associated with the task LRA. We report that conditional
nonlocality necessitates the presence of entangled states in the ensemble, a
feature absent from erstwhile nonlocality arguments based on local state
discrimination. Conversely, all the states in a complete basis set being
entangled implies conditional nonlocality. However, the impossibility of LRA
also exhibits more conditional nonlocality with less entanglement. The relation
between the possibility of LRA and local state discrimination for sets of
multipartite quantum states, both in the perfect and conclusive cases, has also
been established. The results highlight a completely new aspect of the
interplay between the security of information in a network and quantum
entanglement under the LOCC paradigm.
