  Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs
in quantum state discrimination of multipartite separable states. In the
discrimination of orthogonal separable states, the term NLWE is used when the
quantum states cannot be discriminated perfectly by local operations and
classical communication. In this case, the occurrence of NLWE is independent of
nonzero prior probabilities of quantum states being prepared. Recently, it has
been found that the occurrence of NLWE can depend on nonzero prior
probabilities in minimum-error discrimination of nonorthogonal separable
states. Here, we show that even in optimal unambiguous discrimination, the
occurrence of NLWE can depend on nonzero prior probabilities. We further show
that NLWE can occur regardless of nonzero prior probabilities, even if only one
state can be locally discriminated without error. Our results provide new
insights into classifying sets of multipartite quantum states in terms of
quantum state discrimination.
