On small set of one-way LOCC indistinguishability of maximally entangled states

TL;DR

This paper constructs small sets of maximally entangled states in high-dimensional spaces that cannot be distinguished by one-way LOCC, revealing fundamental limits of local quantum state discrimination.

Contribution

It introduces explicit constructions of small sets of maximally entangled states that are indistinguishable via one-way LOCC in any dimension d ≥ 4.

Findings

Constructed sets of size 3⎡√d⎤−1 in dimension d

Proved existence of four maximally entangled states indistinguishable by one-way LOCC for all d ≥ 4

Demonstrated limitations of one-way LOCC in quantum state discrimination

Abstract

In this paper, we study the one-way local operations and classical communication (LOCC) problem. In $\mathbb{C}^d\otimes\mathbb{C}^d$ with $d\geq4$, we construct a set of $3\lceil\sqrt{d}\rceil-1$ one-way LOCC indistinguishable maximally entangled states which are generalized Bell states. Moreover, we show that there are four maximally entangled states which cannot be perfectly distinguished by one-way LOCC measurements for any dimension $d\geq 4$.