# The local distinguishability of any three generalized Bell states

## TL;DR

This paper proves that any three generalized Bell states in a bipartite quantum system of dimension four or higher can be distinguished using local operations and classical communication, advancing understanding of quantum state discrimination.

## Contribution

It establishes that three generalized Bell states are always locally distinguishable in dimensions four and above, filling a gap in quantum state discrimination theory.

## Key findings

- Any three generalized Bell states in $ ext{C}^d imes ext{C}^d$ with $d \\geq 4$ are LOCC distinguishable.
- The result applies to all such states, regardless of their specific form.
- Supports the broader understanding of local distinguishability in quantum information.

## Abstract

We study the problem of distinguishing maximally entangled quantum states by using local operations and classical communication (LOCC). A question of fundamental interest is whether any three maximally entangled states in $\mathbb{C}^d\otimes\mathbb{C}^d (d\geq 4)$ are distinguishable by LOCC. In this paper, we restrict ourselves to consider the generalized Bell states. And we prove that any three generalized Bell states in $\mathbb{C}^d\otimes\mathbb{C}^d (d\geq 4)$ are locally distinguishable.