Polynomial Separation between One-Way and Two-Way LOCC in Discrimination of Maximally Entangled States

One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension d 4. We show that every set of k pairwise orthogonal maximally entangled states in C d C d is perfectly distinguishable by an A to B to A protocol whenever d Ck 4[(2k)] ν, for universal constants C,ν>0. A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to Ω! (d 1/4/(d) ν/4), establishing a polynomial separation between one-way and two-way LOCC. In our protocol, Alice preserves exact orthogonality while reducing overlaps between Bob's conditional subspaces. Bob reduces the candidates to a singleton or an orthogonal pair and refines his outcome so that Alice can complete the discrimination. As a corollary, nine copies suffice for perfect two-way LOCC discrimination of any orthogonal maximally entangled set in all sufficiently large local dimensions.