Three maximally entangled states can require two-way LOCC for local discrimination
School of Science
Physical Review A
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.
SMC Affiliated Work
Michael Nathanson (Mathematics and Computer Science): “Three maximally entangled states can require two-way LOCC for local discrimination,” in Physical Review A 88, 062316 (2013). doi:10.1103/PhysRevA.88.062316
Nathanson, Michael. Three maximally entangled states can require two-way LOCC for local discrimination (2013). Physical Review A. 88 (6), 062316 10.1103/PhysRevA.88.062316 [article]. https://digitalcommons.stmarys-ca.edu/school-science-faculty-works/80