Novel Constructions of Mutually Unbiased Tripartite Absolutely Maximally Entangled Bases

Abstract

We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d\otimes {\mathbb{C}}^d$ based on mutually orthogonal Latin squares. Then we generalize the approach to the case of ${\mathbb{C}}^{d_1}\otimes {\mathbb{C}}^{d_2}\otimes {\mathbb{C}}^{d_1{d}_2}$ by mutually weak orthogonal Latin squares. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably presented with generality. Detailed examples in ${\mathbb{C}}^3\otimes {\mathbb{C}}^3\otimes {\mathbb{C}}^3,$ ${\mathbb{C}}^2\otimes {\mathbb{C}}^2\otimes {\mathbb{C}}^4$ and ${\mathbb{C}}^2\otimes {\mathbb{C}}^5\otimes {\mathbb{C}}^{10}$ are provided to illustrate the advantages of our approach.

References in corpus (2)

• Maximally multipartite entangled states
• Nonmaximally entangled states can be better for multiple linear optical teleportation