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

Abstract

We give a explicit construction of $d$ locally indistinguishable orthogonal maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ for any $d\ge 4$. 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.

The paper is rewrited, especally the introduction. 5 pages, no figures

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