$d$ locally indistinguishable maximally entangled states in $\mathbb{C}^d\otimes\mathbb{C}^d$

TL;DR

This paper constructs explicit examples of $d$ orthogonal maximally entangled states in $ ext{C}^d imes ext{C}^d$ that cannot be distinguished locally, confirming a long-standing conjecture and highlighting quantum nonlocality.

Contribution

It provides the first explicit construction of $d$ locally indistinguishable maximally entangled states for all $d geq 4$, resolving a conjecture from 2009.

Findings

Constructed $d$ locally indistinguishable maximally entangled states for all $d eq 4$

Confirmed the conjecture by S. Bandyopadhyay from 2009

Demonstrated quantum nonlocality through state indistinguishability

Abstract

We give a explicit construction of $d$ locally indistinguishable orthogonal maximally entangled states in $\mathbb{C}^d\otimes\mathbb{C}^d$ for any $d\geq 4$. This gives an answer to the conjecture proposed by S. Bandyopadhyay in 2009. Thus it reflects the nonlocality of the fundamental feature of quantum mechanics.