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 $d\ge4$. 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 $d\ge Ck^4[\log(2k)]^\nu$, 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:2610.04288 [quant-ph]

(or arXiv:2610.04288v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.04288 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.