Suppose I have a set of multipartite orthogonal product bases, which I want to prove as possessing some quantum non locality. i.e they can't be distinguished perfectly with local operations and classical communications. So one way which I found is to show if they are unextendible product base sets, because that implies that states are nonlocal for measurements. But, is the negation also valid? If the set isn't unextendible product bases, then does it imply that the states don't show any quantum non locality?
If by non-locality you mean "not distinguishable using LOCC" than the answer is no. The original paper on the subject [http://arxiv.org/abs/quant-ph/9804053] has the most famous example of a full product basis with a set of states that cannot be discriminated locally.
The converse as you mentioned is not correct as there is a full 3x3 orthogonal basis which is not locally distinguishable(By Bennett et. al.). This construction enables you to form set of many orthogonal product states which are not locally distinguishable.
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