Novel constructions of mutually unbiased tripartite absolutely maximally entangled bases

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 C-d circle times C-d circle times C-d based on mutually orthogonal Latin squares. Then we generalize the approach to the case of C-d1 circle times C-d2 circle times C(d1d2 )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 C-3 circle times C-3 circle times C-3, C-2 circle times C-2 circle times C-4 and C-2 circle times C-5 circle times C-10 are provided to illustrate the advantages of our approach.

Automated summary

We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably presented with generality. Examples in specific cases demonstrate the advantages of our approach.