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

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.

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