We show that there exist sets of three mutually orthogonal d -dimensional maximally entangled states which cannot be perfectly distinguished using one-way local operations and classical communication (LOCC) for arbitrarily large values of d . This contrasts with several well-known families of maximally entangled states, for which any three states can be perfectly distinguished. We then show that two-way LOCC is sufficient to distinguish these examples. We also show that any three mutually orthogonal d -dimensional maximally entangled states can be perfectly distinguished using measurements with a positive partial transpose (PPT) and can be distinguished with one-way LOCC with high probability. These results circle around the question of whether there exist three maximally entangled states which cannot be distinguished using the full power of LOCC; we discuss possible approaches to answer this question.
Physical Review A – American Physical Society (APS)
Published: Dec 12, 2013
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