Three maximally entangled states can require two-way LOCC for local discrimination

Understand

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.