It is not always possible to distinguish multipartite orthogonal states if only local operations and classical communication (LOCC) are allowed. We prove that we cannot distinguish the states of an unextendible product basis by LOCC even with infinite resources (infinite-dimensional ancillas, infinite number of operations). Moreover we give a necessary and sufficient condition for the LOCC distinguishability of a complete product basis.
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S. De Rinaldis (2004) studied this question.
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