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

Abstract

One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension $d\ge 4$. We show that every set of $k$ pairwise orthogonal maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ is perfectly distinguishable by an $A\to B\to A$ protocol whenever $d\ge C{k}^4[\log (2k){]}^{\nu }$, for universal constants $C,\nu >0$. A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to $\Omega \left(d^{1/4}/(\log d{)}^{\nu /4}\right)$, 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.

arXiv comment5+12 pages, 1 figure